1. Treewidth versus clique number. v. further connections with tree‐independence numberClaire Hilaire, Martin Milanič, Ðorđe Vasić, 2026, original scientific article Abstract: We continue the study of (tw, ω)‐bounded graph classes, that is, hereditary graph classes in which large treewidth is witnessed by the presence of a large clique, and the relation of this property to boundedness of the tree‐independence number, a graph parameter introduced independently by Yolov in 2018 and by Dallard, Milanič, and Štorgel in 2024. Dallard et al. showed that bounded tree‐independence number is sufficient for (tw, ω)‐boundedness, and conjectured that the converse holds. While this conjecture has been recently disproved, it is still interesting to determine classes where the conjecture holds; for example, the conjecture is still open for graph classes excluding an induced star, as well as for finitely many forbidden induced subgraphs. In this paper, we identify further families of graph classes where (tw, ω)‐boundedness is equivalent to bounded tree‐independence number. We settle a number of cases of finitely many forbidden induced subgraphs, obtain several equivalent characterizations of (tw, ω)-boundedness in subclasses of the class of complements of line graphs, and give a short proof of a recent result of Ahn, Gollin, Huynh, and Kwon [SODA 2025] establishing bounded tree-independence number for graphs excluding a fixed induced star and a fixed number of independent cycles.
Keywords: clique number, hereditary graph class, line graph, tree‐independence number, treewidth
Published in RUP: 09.04.2026; Views: 190; Downloads: 9
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2. On relationships between treewidth, clique number, tree-independence number, and induced minors : master’s thesisÐorđe Vasić, 2025, master's thesis Keywords: treewidth, clique number, tree-independence number, induced minor, hered itary graph class, bipartite chain graph
Published in RUP: 11.09.2025; Views: 1066; Downloads: 10
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5. Edge elimination schemes of weighted graph classes, Workshop on Graph Modification algorithms, experiments and new problems, 23rd - 24th January 2020, Bergen, NorwayMartin Milanič, Jesse Beisegel, Nina Chiarelli, Ekkehard Köhler, Matjaž Krnc, Nevena Pivač, Robert Scheffler, Martin Strehler, 2020, unpublished invited conference lecture Keywords: graph class, edge elimination scheme, sandwich monotonicity
Published in RUP: 28.05.2020; Views: 3302; Downloads: 0 |
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