A graph is O k-free if it does not contain k pairwise vertex-disjoint and non-adjacent cycles.
We prove that “sparse”(here, not containing large complete bipartite graphs as subgraphs) O …

We continue the study of (tw, ω)-bounded graph classes, that is, hereditary graph classes in
which the treewidth can only be large due to the presence of a large clique, with the goal of …

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 …

A graph G contains a graph H as an induced minor if H can be obtained from G by vertex
deletions and edge contractions. The class of H-induced-minor-free graphs generalizes the …

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 …

Induced Subgraphs and Tree Decompositions VIII: Excluding a Forest in (Theta, Prism)-Free
Graphs | Combinatorica Skip to main content SpringerLink Account Menu Find a journal …

For a tree decomposition $\mathcal {T} $ of a graph $ G $, by $\mu (\mathcal {T}) $ we
denote the size of a largest induced matching in $ G $ all of whose edges intersect one bag …

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 $ K_4 $ by …

The tree‐independence number tree‐α treex02010α, first defined and studied by Dallard,
Milanič, and Štorgel, is a variant of treewidth tailored to solving the maximum independent …

We study how the relationship between non-equivalent width parameters changes once we
restrict to some special graph class. As width parameters, we consider treewidth, clique …