We recently introduced the notion of twin-width, a novel graph invariant, and showed that
first-order model checking can be solved in time for-vertex graphs given with a witness that …

We present an algorithm that takes as input a graph G with weights on the vertices, and
computes a maximum weight independent set S of G. If the input graph G excludes a path P …

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 …

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 …

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 …

In a recent breakthrough work, Gartland and Lokshtanov [FOCS 2020] showed a quasi-
polynomial-time algorithm for Maximum Weight Independent Set in Pt-free graphs, that is …

For an integer t, a graph G is called C> t-free if G does not contain any induced cycle on
more than t vertices. We prove the following statement: for every pair of integers d and t and …

We show that the Maximum Weight Independent Set problem (MWIS) can be solved in quasi-
polynomial time on H-free graphs (graphs excluding a fixed graph H as an induced …

A hole in a graph is an induced cycle of length at least 4. A hole is long if its length is at least
5. By, we denote a path on vertices. In this paper, we give polynomial-time algorithms for the …

For a set of graphs\({\mathcal {H}}\), a graph G is\({\mathcal {H}}\)-subgraph-free if G does
not contain any graph from\({{{\mathcal {H}}}}\) as a subgraph. We propose general and easy …