Konrad K. Dabrowski

Colouring vertices of triangle-free graphs without forests

The vertex colouring problem is known to be NP-complete in the class of triangle-free graphs. Moreover, it is NP-complete in any subclass of triangle-free graphs defined by a finite collection of forbidden induced subgraphs, each of which contains a cycle. In this paper, we study the vertex colouring problem in subclasses of triangle-free graphs obtained by forbidding graphs without cycles, i.e., forests, and prove polynomial-time solvability of the problem in many classes of this type. In particular, our paper, combined with some previously known results, provides a complete description of the complexity status of the problem in subclasses of triangle-free graphs obtained by forbidding a forest with at most 6 vertices.

Clique-Width of Graph Classes Defined by Two Forbidden Induced Subgraphs

If a graph has no induced subgraph isomorphic to any graph in a finite family

Classifying the clique-width of H -free bipartite graphs

\{H_1,\ldots ,H_p\}

Colouring vertices of triangle-free graphs

, it is said to be

Bounding Clique-Width via Perfect Graphs

H_1,\ldots ,H_p

Parameterized complexity of the weighted independent set problem beyond graphs of bounded clique number

-free. The class of