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 …

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 graphs G and H, we say that G is H-free if it does not contain H as an induced subgraph.
Already in the early 1980s Alekseev observed that if H is connected, then the Max Weight …

In the Maximum Independent Set problem we are asked to find a set of pairwise
nonadjacent vertices in a given graph with the maximum possible cardinality. In general …

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 prove that a number of computational problems that ask for the largest sparse induced
subgraph satisfying some property definable in CMSO2 logic, most notably Feedback Vertex …

We revisit the recent polynomial-time algorithm for the MAX WEIGHT INDEPENDENT SET
(MWIS) problem in bounded-degree graphs that do not contain a fixed graph whose every …

We revisit recent developments for the Maximum Weight Independent Set problem in graphs
excluding a subdivided claw S t, t, t as an induced subgraph and provide a subexponential …