Browsing University of Waterloo by Author "Hajebi, Sepehr"
Now showing items 1-9 of 9
-
Complexity Dichotomy for List-5-Coloring with a Forbidden Induced Subgraph
Hajebi, Sepehr; Li, Yanjia; Spirkl, Sophie (Society for Industrial and Applied Mathematics, 2022-08-30)For a positive integer r and graphs G and H, we denote by G+H the disjoint union of G and H and by rH the union of r mutually disjoint copies of H. Also, we say G is H-free if H is not isomorphic to an induced subgraph of ... -
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, 2024-01)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. Three-Path-Configurations and Logarithmic Treewidth.
Abrishami, Tara; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie (Advances in Combinatorics, 2022-09-09)A theta is a graph consisting of two non-adjacent 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 H-free 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, 2023-06-16)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 H-free graphs.
Abrishami, Tara; Alecu, Bogdan; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie (Elsevier, 2024-01)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, 2024-04-08)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. -
List-3-Coloring Ordered Graphs with a Forbidden Induced Subgraph
Hajebi, Sepehr; Li, Yanjia; Spirkl, Sophie (Society for Industrial and Applied Mathematics, 2024-03)Abstract. The List-3-Coloring Problem is to decide, given a graph G and a list L(v) ⊆ {1, 2, 3} of colors assigned to each vertex v of G, whether G admits a proper coloring ϕ with ϕ(v) ∈ L(v) for every vertex v of G, and ... -
Minimal induced subgraphs of two classes of 2-connected non-Hamiltonian graphs
Cheriyan, Joseph; Hajebi, Sepehr; Qu, Zishen; Spirkl, Sophie (Elsevier, 2022-07)In 1981, Duffus, Gould, and Jacobson showed that every connected graph either has a Hamiltonian path, or contains a claw (K1,3) or a net (a fixed six-vertex graph) as an induced subgraph. This implies that subject to being ... -
Tree independence number I. (Even hole, diamond, pyramid)-free graphs
Abrishami, Tara; Alecu, Bogdan; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie; Vuskovic, Kristina (Wiley, 2024-04-24)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. ...