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Now showing items 1-6 of 6

• #### Induced subgraphs and tree decompositions II. Toward walls and their line graphs in graphs of bounded degree. ﻿

(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. ﻿

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 ﻿

(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. ﻿

(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 ﻿

(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.
• #### Tree independence number I. (Even hole, diamond, pyramid)-free graphs ﻿

(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. ...

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