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 …

Polar graphs are a common generalization of bipartite, cobipartite, and split graphs. They
are defined by the existence of a certain partition of vertices, which is NP-complete to decide …

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 …

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 …

Abstract This thesis considers Efficient Domination, Efficient Edge Domination, Polarity, and
Monopolarity, graph problems that ask for a vertex or edge subset that is a packing and a …

Polar graphs generalise bipartite, cobipartite, split graphs, and they constitute a special type
of matrix partitions. A graph is polar if its vertex set can be partitioned into two, such that one …

Polar and monopolar graphs are natural generalizations of bipartite and split graphs. A
graph G=(V, E) is polar if its vertex set admits a partition V= A∪ B such that A induces a …