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 …

The independence number of a tree decomposition is the maximum of the independence
numbers of the subgraphs induced by its bags. The tree-independence number of a graph is …

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 …

In 2020, we initiated a systematic study of graph classes in which the treewidth can only be
large due to the presence of a large clique, which we call (tw, ω)-bounded. The family of (tw …

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 …

We prove that the tree independence number of every even-hole-free graph is at most
polylogarithmic in its number of vertices. More explicitly, we prove that there exists a …

A vertex in a graph is simplicial if its neighborhood forms a clique. We consider three
generalizations of the concept of simplicial vertices: avoidable vertices (also known as OCF …

We continue the study of graph classes in which the treewidth can only be large due to the
presence of a large clique, and, more specifically, of graph classes with bounded tree …

We propose a novel way of generalizing the class of interval graphs, via a graph width
parameter called the simultaneous interval number. This parameter is related to the …

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 …