Year: 2025
Type: article
Abstract: We construct classes of graphs that are variants of the so-called layered wheel . One of their key properties is that while the treewidth is bounded by a function of the clique number, the construction can be adjusted to make the dependence grow arbitrarily. Some of these classes provide counter-examples to several conjectures. In particular, the construction includes hereditary classes of graphs whose treewidth is bounded by a function of the clique number while the tree-independence number is unbounded, thus disproving a conjecture of Dallard, Milanič and Štorgel [Treewidth versus clique number. II. Tree-independence number. Journal of Combinatorial Theory, Series B , 164:404–442, 2024]. The construction can be further adjusted to provide, for any fixed integer c , graphs of arbitrarily large treewidth that contain no K c -free graphs of high treewidth, thus disproving a conjecture of Hajebi [Chordal graphs, even-hole-free graphs and sparse obstructions to bounded treewidth, arXiv:2401.01299, 2024].
Source: Innovations in Graph Theory
DOI: 10.5802/igt.11
Authors: Maria Chudnovsky, Nicolas Trotignon
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Awards: G1523888516, G169068394, PROJET AVENIR LYON SAINT-ETIENNE, G3010527862, Community of mathematics and fundamental computer science in Lyon, G3800539971, G3824936037, G4866930200, Digraphs, DMS-EPSRC: The Power of Graph Structure, G5045220161, Forbidding Induced Subgraphs: Decompositions, Coloring and Algorithms, G6494969328, G7240651115, G9575639
OpenAlex ID: W4414623783