Browsing Waterloo Research by Author "Abrishami, Tara"
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Induced subgraphs and tree decompositions II. Toward walls and their line graphs in graphs of bounded degree.
Abrishami, Tara; Chudnovsky, Maria; Dibek, Cemil; Hajebi, Sepehr; Rzqzewski, Pawel; Spirkl, Sophie; Vuskovic, Kristina (Elsevier, 202401)This paper is motivated by the following question: what are the unavoidable induced subgraphs of graphs with large treewidth? Aboulker et al. made a conjecture which answers this question in graphs of bounded maximum ... 
Induced Subgraphs and Tree Decompositions III. ThreePathConfigurations and Logarithmic Treewidth.
Abrishami, Tara; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie (Advances in Combinatorics, 20220909)A theta is a graph consisting of two nonadjacent vertices and three internally disjoint paths between them, each of length at least two. For a family H of graphs, we say a graph G is Hfree if no induced subgraph of G is ... 
Induced Subgraphs and Tree Decompositions IV. (Even Hole, Diamond, Pyramid)Free Graphs
Abrishami, Tara; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie (Electronic Journal of Combinatorics, 20230616)A hole in a graph G is an induced cycle of length at least four, and an even hole is a hole of even length. The diamond is the graph obtained from the complete graph K4 by removing an edge. A pyramid is a graph consisting ... 
Induced subgraphs and tree decompositions VII. Basic obstructions in Hfree graphs.
Abrishami, Tara; Alecu, Bogdan; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie (Elsevier, 202401)We say a class C of graphs is clean if for every positive integer t there exists a positive integer w(t) such that every graph in C with treewidth more than w(t) contains an induced subgraph isomorphic to one of the ... 
Induced Subgraphs and Tree Decompositions VIII: Excluding a Forest in (Theta, Prism)Free Graphs
Abrishami, Tara; Alecu, Bogdan; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie (Springer, 20240408)Given a graph H, we prove that every (theta, prism)free graph of sufficiently large treewidth contains either a large clique or an induced subgraph isomorphic to H, if and only if H is a forest. 
Tree independence number I. (Even hole, diamond, pyramid)free graphs
Abrishami, Tara; Alecu, Bogdan; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie; Vuskovic, Kristina (Wiley, 20240424)The tree‐independence number tree‐α, first defined and studied by Dallard, Milanič, and Štorgel, is a variant of treewidth tailored to solving the maximum independent set problem. Over a series of papers, Abrishami et al. ...