Browsing by Author "Chudnovsky, Maria"

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    Induced subgraphs and tree decompositions VI. Graphs with 2-cutsets
    (Elsevier, 2025-01) Abrishami, Tara; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie
    This paper continues a series of papers investigating the following question: which hereditary graph classes have bounded treewidth? We call a graph t-clean if it does not contain as an induced subgraph the complete graph Kt, the complete bipartite graph Kt,t, subdivisions of a (t x t)-wall, and line graphs of subdivisions of a (t x t)-wall. It is known that graphs with bounded treewidth must be t-clean for some t; however, it is not true that every t-clean graph has bounded treewidth. In this paper, we show that three types of cutsets, namely clique cutsets, 2-cutsets, and 1-joins, interact well with treewidth and with each other, so graphs that are decomposable by these cutsets into basic classes of bounded treewidth have bounded treewidth. We apply this result to two hereditary graph classes, the class of (ISK4, well)-free graphs and the class of graphs with no cycle with a unique chord. These classes were previously studied and decomposition theorems were obtained for both classes. Our main results are that t-clean (ISK4, wheel)-free graphs have bounded treewidth and that t-clean graphs with no cycle with a unique chord have bounded treewidth.
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    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.