A graph H is an induced minor of a graph G if H can be obtained from G by vertex deletions
and edge contractions. We show that there is a function f (k, d)= O (k 10+ 2 d 5) so that if a …

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 …

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 …

A graph $ H $ is an induced subgraph of a graph $ G $ if a graph isomorphic to $ H $ can be
obtained from $ G $ by deleting vertices. Recently, there has been significant interest in …

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 …

Many recent works address the question of characterizing induced obstructions to bounded
treewidth. In 2022, Lozin and Razgon completely answered this question for graph classes …

Treewidth is a fundamental graph parameter that quantifies the complexity of graphs by
measuring their" thickness" compared to a tree. In 1986, Robertson and Seymour proved …

A circle graph is an intersection graph of a set of chords of a circle. We describe the
unavoidable induced subgraphs of circle graphs with large treewidth. This includes …

What are the unavoidable induced subgraphs of graphs with large treewidth? It is well‐
known that the answer must include a complete graph, a complete bipartite graph, all …

A generalized $ t $-pyramid is a graph obtained from a certain kind of tree (a subdivided star
or a subdivided cubic caterpillar) and the line graph of a subdivided cubic caterpillar by …