We discuss partition problems that generalize graph colouring and homomorphism
problems, and occur frequently in the study of perfect graphs. Depending on the pattern, we …

Abstract A graph G=(V, E) is a unipolar graph if there exists a partition V= V 1∪ V 2 such that
V 1 is a clique and V 2 induces the disjoint union of cliques. The complement-closed class of …

We show that one can compute the injective chromatic number of a chordal graph G at least
as efficiently as one can compute the chromatic number of (G− B) 2, where B are the bridges …

In this paper, we develop a divide-and-conquer approach, called block decomposition, to
solve the minimum geodetic set problem. This provides us with a unified approach for all …

A graph is called split if its vertex set can be partitioned into a stable set and a clique. In this
article, we studied two variants of split graphs. A graph G is polar if its vertex set can be …

Polar, monopolar, and unipolar graphs are defined in terms of the existence of certain vertex
partitions. Although it is polynomial to determine whether a graph is unipolar and to find …

A graph $ G=(V, E) $ is said to be monopolar if its vertex set admits a partition $ V=(C\uplus
{} I) $ where $ G [C] $ is a cluster graph and $ I $ is an independent set in $ G $. Monopolar …

We consider classes of graphs, which we call thick graphs, that have their vertices replaced
by cliques and their edges replaced by bipartite graphs. In particular, we consider the case …

Polarity and monopolarity are properties of graphs defined in terms of the existence of
certain vertex partitions; graphs with polarity and monopolarity are respectively called polar …

The generalized graph colouring problem (GCOL) for a fixed integer k, and fixed classes of
graphs P_1,..., P_k (usually describing some common graph properties), is to decide, for a …