Waterloo Research

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Microstructural Evolution and Formation Mechanism of the Halo Ring in Resistance Spot Welding of a 3G Advanced High Strength Steel
(Springer, 2024-09-09) Ramachandran, Dileep Chandran; Salandari-Rabori, Adib; Macwan, Andrew; Biro, Elliot
The microstructure of the halo ring has been studied in quenched and partitioned (Q&P) steel resistance spot welds. The TEM and EBSD characterizations revealed the presence of an upper bainitic microstructure in the halo ring of the three-sheet stack-up welds. Stalking faults accompanied by nano-twins were identified surrounding the cementite. Diffusion of carbon towards the molten weld pool during solidification led to the formation of bainite at the fusion boundary, triggered the localized softening.
Effect of Paint Baking Treatment on Mechanical Properties of Resistance Spot Welded Q&P 980 Steel
(ISIJ International, 2024-05-15) Ramachandran, Dileep Chandran; Salandari-Rabori, Adib; Midawi, Adbelbaset R.H.; Macwan, Andrew; Biro, Elliot
This study investigates the impact of paint baking on the macro and micro-mechanical properties of resistance spot welds in quenched and partitioned 980 steels. It is observed that paint baking enhances both peak load and energy absorption during cross-tension tests, as indicated by load-displacement curves. Four different regions were identified from the load-displacement curves after paint baking. An intriguing observation was a quick increase in the loading rate following a prior decrease, attributed to change in crack propagation behavior rather than improved work hardening. The study further simulated the upper-critical heat-affected zone using a Gleeble thermo-mechanical simulator to evaluate flow strength and work hardening. The Kocks-Mecking strain-hardening model was employed to analyze work hardening behavior in the studied conditions.
Effect of Paint Baking on the Fusion Boundary Softening and Fracture Behavior of Q&P 980 Steel Resistance Spot Welds
(Elsevier, 2023-10-14) Ramachandran, Dileep Chandran; Betiku, Olakunle Timothy; Shojaee, Mohammad; Salandari-Rabori, Adib; Midawi, Abdelbaset R.H.; Kim, Ji-Ung; Bakhtiari, Reza; Macwan, Andrew; Biro, Elliot
During automotive assembly, vehicles undergo low-temperature heat treatment (paint baking) to harden the paint. Although paint baking occurs at a relatively low temperature, it can remarkably affect the weld's mechanical and fracture behavior. This work studies how paint baking improving the strength and fracture behavior of Q&P 980 spot welds exhibiting a halo ring; a low carbon enriched zone in the weld nugget. The mechanical behavior of the paint-baked welds reveals an increase in cross-tensile strength and absorbed energy when baked at 180 °C for 27 min. Microstructural observation showed that the martensite present in the as-welded conditions started to decompose into tempered martensite with ε-carbide in the martensitic matrix. Gleeble thermo-mechanical simulations of the upper-critical heat-affected zone (UCHAZ) were produced to understand the mechanical and fracture micro-and macro-mechanisms, before and after the paint baking process, by widening the regions of UCHAZ. The transmission electron microscopic analysis of the Gleeble simulated sample reveals the segregation of C, Mn, Al, and Cr along the prior austenitic grain boundary which will change the nature of bonding at these boundaries. Nevertheless, paint baking treatment helps to redistribute the segregated elements from the grain boundary to the grain interior and to eliminate the solidified liquation formed at the grain boundaries during welding. The transformation of martensite to decomposed martensite, elimination of solidified liquation due to the enhanced atomic mobility and growth of surrounding grains, and the redistribution of C, Mn, Al, and Cr from the grain boundary to interior regions of grains, are the main reasons for the improvement of mechanical properties and fracture behavior of the spot welds.
A Study on Improving the Mechanical Performance by Controlling the Halo Ring in the Q&P 980 Steel Resistance Spot Welds
(Elsevier, 2022-01-17) Ramachandran, Dileep Chandran; Figueredo, Bruna; Sherepenko, Oleksii; Jin, Woosung; Park, Yeong-Do; Biro, Elliot
This study focuses on improving the mechanical performance of third-generation Q&P steel resistance spot welds using a double-pulse welding cycle. Single and double-pulse welding schedules were implemented to assess the mechanical performance of the welds. Single-pulse welds exhibited poor cross-tension strength (CTS) values, failed around the fusion zone, and were accompanied by poor energy absorption capability. However, the double-pulse schedule showed improved CTS values by 33%, with an associated 110% increase in absorbed energy. The failure path observed from interrupted cross-tension tests showed that, in welds made using both pulsing schedules, failure proceeded along the fusion boundary and CGHAZ. In the single-pulse welds failed in brittle fashion, whereas the welds made with a double-pulse schedule exhibited a mixed (ductile and brittle) fracture morphology. The high-density microhardness mapping confirmed the presence of a localized softened zone (halo ring) adjacent to the fusion boundary in single-pulse welds. Strong elemental partitioning of Mn, Si, and C in the vicinity of the fusion boundary during long welding time was the primary cause for the halo formation. However, the halo ring was eliminated by performing a double-pulse weld schedule with 30 ms cooling time in between pulses; resulting in improved mechanical properties.
Planting Imagination: Community Co-Design 'How-to-Guide'
(2024-01-01) Zhang, Linda; Fox, Tyler
This How-to Guide details how a group of architects, residents, community organizers, and public health researchers embarked on a journey to explore more radical ways of designing, working, and building together. Our aim was to go beyond the usual (and at times disempowering) community consultation methods commonly used in neighbourhood design, to see if we can develop an ethical co-design approach that starts and ends with the local community. Through a combination of virtual reality (VR) centric visioning sessions and co-design workshops, we worked together to redesign Cecil’s community garden located in Toronto’s Chinatown West. This process helped us build community power to address ‘neighbourhood health’ as a collective resource in the context of COVID-19, and encouraged us to think beyond individualized health outcomes. This guide is our way of sharing what we learned. We hope to encourage others to design and build in a more authentic and generative way by collaborating with local communities, and be open to bringing together diverse skills, practices, knowledge, and people. We’re excited to see how you might take, build, and make use of our insights in your own work and community. Let’s get started! 本操作指南将详细介绍一群建筑师、居民、社区组织者和公共卫生研究人员如何踏上探索更激进的共同设计、工作和建设方式的旅程。我们的目标是超越社区设计中常用（有时让人感到无能为力）的社区咨询方法，看看我们能否开发一种有道德和以当地社区为起与终点的共同设计方法。通过以虚拟现实 (VR) 为中心的愿景构想会议和共同设计活动，我们協力改造了位于多伦多西区唐人街思豪社区花园的设计。这过程帮助了我们建立社区力量以呼应在COVID-19背景下将“社区健康”作为集体资源看待，并鼓励我们进行超越个人健康结果的思考。本指南是我们分享所学的方式。我们希望鼓励其他人通过与当地社区合作来达到更真实，更具创造性的方式进行设计和建造，并接纳将不同的技能、实践、知识和人才汇集在一起。我们很期待看到您如何在自己的工作和社区中收取，构建和利用我们的见解。让我们开始吧！
Rolling in Fun, Paying the Price: A Thematic Analysis on Purchase and Play in Tabletop Games
(Association for Computing Machinery New York, NY, United States, 2024-12-12) Joseph Tu; Derrick Wang; Lydia Choong; Aj Abistado; Stuart Hallifax; Katja Rogers; Lennart Nacke
The tabletop games industry has experienced remarkable growth in recent years. A deeper exploration of the factors motivating players to invest time and money in these games would help game companies better cater to their target audience and increase profits. We conducted a reflexive thematic analysis of 20 semi-structured interviews with tabletop game players. Our analysis revealed five themes concerning purchasing decision influences: (1) childhood past experiences and cultural norms, (2) representation and inclusivity, (3) social connections and shared fun, (4) overcoming gameplay hindrances with digital assistance, and (5) economic constraints. These findings suggest that game companies should focus on presenting easily understandable information, minimizing idle time, and exploring opportunities for inclusivity in digital interactions to effectively engage players and drive sales. Based on our valuable insights into player motivations, we offer actionable recommendations for the tabletop games industry.
A Comprehensive Evaluation of Tempering Kinetics on 3rd Generation Advanced High Strength Steels
(Elsevier, 2022-12-02) Dileep Chandran Ramachandran; Elliot Biro
Emerging third-generation advanced high strength steels (3G AHSS) grades are being increasingly considered for autobody applications owing to their complex microstructures providing an excellent combination of strength and ductility. When welded with RSW, 3G AHSS such as 3G 1180 and 3G 980, exhibits a solid-state transformation in the sub-critical-heat-affected-zone (SCHAZ) due to the heat generated during the RSW process. The resulting changes in microstructure can affect the mechanical properties of the material within and around the spot welds and thereby influence the performance of welded components in case of a vehicle crash event. To study metallurgical transformations in the SCHAZ during the RSW process, 3G 1180 and 3G 980, and a reference martensitic press hardened steel, PHS 1500, were selected. These materials were subjected to isothermal tempering experiments at temperatures ranging between 350 °C and 650 °C and different tempering times from 0.2 s to 24 h. It was shown that the Hollomon-Jaffe model accurately describes the tempering kinetics of 3G 1180 and PHS 1500 but does not predict the transformation processes in the SCHAZ of 3G 980. The PHS 1500 and 3G 1180 showed softening (tempering) for all combinations of investigated tempering times and temperatures due to the decomposition of martensite. In contrast, the 3G 980 showed a combination of softening by the formation of martensite and secondary ferrite combined with secondary hardening due to the formation of fine M2C typed plate-like carbides. Furthermore, during long tempering, the M2C particles dissolve into the matrix and were replaced by cementite particles in 3G 980.
Effect of Material Chemical Composition on the Formation of Halo Ring in Gen 3 Q&P 980 Steel
(Springer, 2024-12-17) Dileep Chandran Ramachandran; Elliot Biro
This study investigates how fusion zone (FZ) chemical composition influences the formation of the halo ring, a transient softening region that can form along the fusion boundary (FB) of resistance spot welds in Q&P980. For this purpose, spot welds were made in both similar Q&P steel joints as well as joints sandwiching low carbon (LC) or high carbon (HC) steels with Q&P steels, which tailored the chemical composition of the FZ. Electron probe microanalysis (EPMA) characterization was performed on a spot-welded sample to understand the effect of material chemical composition on the halo formation. Alloying elements such as C, Mn, and Si were significantly less in the FZ composition of the welds made with LC steel, as compared to 3-sheet Q&P weld, which resulted in associated 33% reduction in hardness of the LC steel FZ. On the contrary, the C and Mn were higher in the FZ of the weld made with HC steel compared to that of the 3-sheet Q&P weld. However, like the welds made with the LC steel the FZ of the welds with the HC steel had a lower Si content than the FZ of the 3-sheet Q&P steel. The increase in C and Mn contents in the welds made with the HC steel resulted in an 14% increase in FZ hardness compared to the FZ of the 3-sheet Q&P steel. The halo formation is more prominent in welds made with LC steel. It was wider in welds where the FZ had a lower alloy content than the Q&P steel as compared to the higher alloyed FZ of the weld made with the HC steel. In LC steel weld a high Mn and Si segregated region inside the FZ was also observed. It was shown that the transient softened zone can be affected by the difference in chemical composition between the FZ and heat-affected zone (HAZ). Therefore, any changes in mechanical properties associated with the halo are more likely to be more prominent in dissimilar welds where high and low alloy steels are combined.
Securing Public Interest Cybersecurity Researchers in Canadian Universities
(University of Ottawa Press, 2024) Molnar, Adam
Rooted in democratic ideals, public interest cybersecurity research is essential for understanding the complex relationship between cybersecurity, human rights, and social justice. Universities, with their long tradition of independent inquiry, provide a crucial space for challenging the dominant influence of private industry in shaping our understanding of cybersecurity. Researchers in these institutions are uniquely positioned to generate knowledge that goes beyond profit-driven narratives and encompass a wider range of concerns, including those of civil society organizations, activists, journalists, and marginalized communities. However, researchers employing established computer security methods in public interest cybersecurity work at Canadian universities face their own crisis of the “security of self” due to substantial legal uncertainties surrounding the lawful permissibility of their research. These uncertainties not only threaten the personal and professional security of researchers, but also hinders the ability to contribute to a broader critical understanding of cybersecurity risks, ultimately limiting our collective “security of self” in the digital age. Building upon Deibert’s (2018) call for a human-centric approach to cybersecurity that prioritizes digital security alongside public interest values, this chapter argues that the legal ambiguities surrounding cybersecurity research in Canadian universities threaten researchers’ ability to conduct meaningful research in the public interest. It examines common methodological practices in this field and their interaction with legal considerations, exploring implications under criminal and copyright law, as well as civil issues like breach of contract and negligence. By scrutinizing potential interpretations of computer security methods under relevant law, the chapter highlights the need to protect researchers and foster an environment conducive to critical knowledge production in human-centred cybersecurity. Ultimately, it poses a series of recommendations for governments to strengthen legal safeguards for public interest cybersecurity research in Canadian universities.
Culture Clash: When Deceptive Design Meets Diverse Player Expectations
(Association for Computing Machinery, 2024-10-14) Hadan, Hilda; Sgandurra, Sabrina; Zhang-Kennedy, Leah; Nacke, Lennart
Deceptive game designs that manipulate players are increasingly common in the gaming industry, but the impact on players is not well studied. While studies have revealed player frustration, there is a gap in understanding how cultural attributes affect the impact of deceptive design in games. This paper proposes a new research direction on the connection between the representation of culture in games and player response to deceptive designs. We believe that understanding the interplay between cultural attributes and deceptive design can inform the creation of games that are ethical and entertaining for players around the globe.
Computer-based Deceptive Game Design in Commercial Virtual Reality Games: A Preliminary Investigation
(Association for Computing Machinery, 2024-10-14) Hadan, Hilda; Zhang-Kennedy, Leah; Nacke, Lennart
As Virtual Reality (VR) games become more popular, it is crucial to understand how deceptive game design patterns manifest and impact player experiences in this emerging medium. Our study sheds light on the presence and effects of manipulative design techniques in commercial VR games compared to a traditional computer game. We conducted an autoethnography study and developed a VR Deceptive Game Design Assessment Guide based on a critical literature review. Using our guide, we compared how deceptive patterns in a popular computer game are different from two commercial VR titles. While VR’s technological constraints, such as battery life and limited temporal manipulation, VR’s unique sensory immersion amplified the impact of emotional and sensory deception. Current VR games showed similar but evolved forms of deceptive design compared to the computer game. We forecast more sophisticated player manipulation as VR technology advances. Our findings contribute to a better understanding of how deceptive game design persists and escalates in VR. We highlight the urgent need to develop ethical design guidelines for the rapidly advancing VR games industry.
Reconsidering the Trade-off between Speed and Accuracy: The Role of Perceived Goal Progress Velocity
(Springer Nature, 2024-11-12) Beck, James W.; Scholer, Abigail A.; Hughes, Jeffrey; Phan, Vincent
Previous research has found a consistent trade-off between speed and accuracy. Whereas completing work tasks quickly is generally associated with increased mistakes, slowing down allows individuals to work in a more careful and accurate manner. However, this previous work has not considered the implications that subjective speed perceptions have for accuracy. To this end, we draw on control theory accounts of goal progress velocity, which predict that feeling slow is associated with negative emotional experiences. We argue that slow perceived progress is frustrating, and that this frustration can hinder accuracy. We tested our hypotheses using an experiment in which participants (N = 92) completed a work simulation. Importantly, actual speed was held constant across conditions, and instead we manipulated participants’ subjective interpretations of their rate of progress. As expected, feeling slow was associated with increased frustration, which in turn was negatively associated with accuracy. The results of this study imply that, contrary to the typical finding of a trade-off between speed and accuracy, there are situations in which slowing down can actually hinder accuracy. Therefore, the current research adds important nuance to the literature on speed-accuracy trade-offs. Additionally, this research provides the most direct test of control theory predictions regarding velocity to date. We conclude with a discussion of the implications of these results for both theory and practice.
The wood frog (Rana sylvatica): An emerging comparative model for anuran immunity and host-ranavirus interactions
(Elsevier, 2023-10) Douglas, Alexander; Katzenback, Barbara
The wood frog (Rana sylvatica) is widely distributed across North America and is the only amphibian found north of the Arctic Circle due to its remarkable ability to tolerate whole-body freezing. Recent mass mortalities attributable to Ranavirus spp. (family Iridoviridae) in wild juvenile wood frogs, coupled with the apparent high susceptibility of wood frogs to experimental infection with frog virus 3 (FV3), the type species of the Ranavirus genus, or FV3-like isolates underscore the serious threat ranaviruses poses to wood frog populations. Despite the ecological relevance and unique life history of wood frogs, our understanding of the wood frog immune system and antiviral response to ranaviral infections is in its infancy. Here we aim to (1) synthesize the limited knowledge of wood frog immune defences, (2) review recent progress in establishing the wood frog as a study system for ranavirus infection, and (3) highlight the future use of wood frogs as a model anuran to provide insight into the evolution of anuran immune systems and antiviral responses.
Composition of the North American Wood Frog (Rana sylvatica) Bacterial Skin Microbiome and Seasonal Variation in Community Structure
(Springer Nature, 2020-07-01) Douglas, Alexander; Hug, Laura; Katzenback, Barbara
While a number of amphibian skin microbiomes have been characterized, it is unclear how these communities might vary in response to seasonal changes in the environment and the corresponding behaviors that many amphibians exhibit. Given recent studies demonstrating the importance of the skin microbiome in frog innate immune defense against pathogens, investigating how changes in the environment impact the microbial species present will provide a better understanding of conditions that may alter host susceptibility to pathogens in their environment. We sampled the bacterial skin microbiome of North American wood frogs (Rana sylvatica) from two breeding ponds in the spring, along with the bacterial community present in their vernal breeding pools, and frogs from the nearby forest floor in the summer and fall to determine whether community composition differs by sex, vernal pond site, or temporally across season (spring, summer, fall). Taxon relative abundance data reveals a profile of bacterial phyla similar to those previously described on anuran skin, with Proteobacteria, Bacteroidetes, and Actinobacteria dominating the wood frog skin microbiome. Our results indicate that sex had no significant effect on skin microbiota diversity, however, this may be due to our limited female frog sample size. Vernal pool site had a small but significant effect on skin microbiota, but skin-associated communities were more similar to each other than to the communities observed in the frogs’ respective pond water. Across seasons, diversity analyses suggest there are significant differences between the bacterial skin microbiome of frogs from spring and summer/fall groups while the average α-diversity per frog remained consistent. These results illustrate seasonal variation in wood frog skin microbiome structure and highlight the importance of considering temporal trends in an amphibian microbiome, particularly for species whose life history requires recurrent shifts in habitat and behavior.
The amphibian invitrome: Past, present, and future contributions to our understanding of amphibian immunity
(Elsevier, 2023-05) Douglas, Alexander; Todd, Lauren; Katzenback, Barbara
Many amphibian populations are declining worldwide, and infectious diseases are a leading cause. Given the eminent threat infectious diseases pose to amphibian populations, there is a need to understand the host-pathogen-environment interactions that govern amphibian susceptibility to disease and mortality events. However, using animals in research raises an ethical dilemma, which is magnified by the alarming rates at which many amphibian populations are declining. Thus, in vitro study systems such as cell lines represent valuable tools for furthering our understanding of amphibian immune systems. In this review, we curate a list of the amphibian cell lines established to date (the amphibian invitrome), highlight how research using amphibian cell lines has advanced our understanding of the amphibian immune system, anti-ranaviral defence mechanisms, and Batrachochytrium dendrobatidis replication in host cells, and offer our perspective on how future use of amphibian cell lines can advance the field of amphibian immunology.
Web Accessibility baby steps: anyone can conduct audits even with limited resources
(2024-07-17) Cefrin da Silva, Israel Jose; Voichita, Stefaniada; Sivakumaran, Mayuri
In today's digital landscape of academic libraries, web accessibility has become a legal requirement under different legislation. Ensuring equal access to digital scholarship, and online library services of libraries for people, with or without disabilities, is crucial. However, conducting web accessibility audits even on our own websites can seem daunting or too tech savvy, especially for individuals with limited technical expertise and resources to afford expensive monitoring tools. This poster, titled "Web Accessibility baby steps: anyone can conduct audits even with limited resources," aims to show how to run basic but effective accessibility audits in a sustainable manner. The main goal is to demonstrate that, using an easy approach, anyone in the library can perform an initial but comprehensive web accessibility audit. It is focused on manual testing techniques, particularly keyboard-only testing which makes the process accessible to all. The process is structured into 3 critical components as follows: Tabbing Order: how to assess tabbing order to ensure logical navigation. Tab Focus: the importance of visible focus indicators and how to verify their effectiveness using a keyboard. Linking/button elements: We explain how to assess link accessibility and activate links using only a keyboard. For those who would like to dive deeper into the subject, they will be provided with links to valuable accessibility tools, guides, and tutorials.
Antarctic basal environment shaped by high-pressure flow through a subglacial river system
(Springer Nature, 2022-10-27) Dow, Christine F.; Ross, Neil; Jeofry, Muhammad Hafeez; Siu, Kevin; Siegert, Martin J.
The stability of ice sheets and their contributions to sea level are modulated by high-pressure water that lubricates the base of the ice, facilitating rapid flow into the ocean. In Antarctica, subglacial processes are poorly characterized, limiting understanding of ice-sheet flow and its sensitivity to climate forcing. Here, using numerical modelling and geophysical data, we provide evidence of extensive, up to 460 km long, dendritically organized subglacial hydrological systems that stretch from the ice-sheet interior to the grounded margin. We show that these channels transport large fluxes (~24 m3 s−1) of freshwater at high pressure, potentially facilitating enhanced ice flow above. The water exits the ice sheet at specific locations, appearing to drive ice-shelf melting in these areas critical for ice-sheet stability. Changes in subglacial channel size can affect the water depth and pressure of the surrounding drainage system up to 100 km either side of the primary channel. Our results demonstrate the importance of incorporating catchment-scale basal hydrology in calculations of ice-sheet flow and in assessments of ice-shelf melt at grounding zones. Thus, understanding how marginal regions of Antarctica operate, and may change in the future, requires knowledge of processes acting within, and initiating from, the ice-sheet interior.
Totten Glacier subglacial hydrology determined from geophysics and modeling
(Elsevier, 2020-02-01) Dow, Christine F.; McCormack, Felicity S.; Young, Duncan A.; Greenbaum, Jamin S.; Roberts, Jason L.; Blankenship, Donald D.
Aurora Subglacial Basin (ASB), which feeds Totten Glacier, is a marine basin lying below sea level and contains up to 3.5 m of global sea level equivalent. Rates of future sea level rise from this area are primarily dependent on the stability of Totten Ice Shelf and the controls on ice flow dynamics upstream of the grounding line, both of which may be influenced by subglacial hydrology. We apply the GlaDS subglacial hydrology model to ASB to examine whether the spatial patterns of distributed and efficient drainage systems impact the dynamics of Totten Glacier. We determine the most appropriate model configuration from our series of sensitivity tests by comparing the modeled basal water pressure and water depth results with specularity content data. Those data are derived from ICECAP radar surveys over the same region and represent regions of basal water accumulation. The best match between simulated basal hydrology properties and specularity content shows a strong correspondence in regions of distributed water in the ASB troughs for both water depth and water pressure, but weak correspondence between water depth and specularity content near the grounding line. This may be due to the presence of several large channels draining over the grounding line into the head of Totten Ice Shelf, which are likely not as well represented in the specularity content data as distributed systems. These channels may have a significant impact on melt, and therefore the stability, of Totten Ice Shelf. Within ASB, regions of high water pressure and greater water accumulation correspond well with regions of faster ice flow, suggesting some control of basal hydrology on ice dynamics in this region.
Induced subgraphs and tree decompositions XIV. Non-adjacent neighbours in a hole.
(Elsevier, 2025-02) Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie
A clock is a graph consisting of an induced cycle C and a vertex not in C with at least two non-adjacent neighbours in C. We show that every clock-free graph of large treewidth contains a "basic obstruction" of large treewidth as an induced subgraph: a complete graph, a subdivision of a wall, or the line graph of a subdivision of a wall.
Polynomial Bounds for Chromatic Number. IV: A Near-polynomial Bound for Excluding the Five-vertex Path.
(Springer, 2023-09-15) Scott, Alex; Seymour, Paul; Spirkl, Sophie
A graph G is H -free if it has no induced subgraph isomorphic to H. We prove that a P5-free graph with clique number ω ≥ 3 has chromatic number at most ωlog2(ω). The best previous result was an exponential upper bound (5/27)3ω, due to Esperet, Lemoine, Maffray, and Morel. A polynomial bound would imply that the celebrated Erd˝os-Hajnal conjecture holds for P5, which is the smallest open case. Thus, there is great interest in whether there is a polynomial bound for P5-free graphs, and our result is an attempt to approach that.

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