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, 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 …

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 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 …

The list monopolar partition problem asks whether a graph G together with lists L (v)⊆{0, 1},
v∈ V (G) admits a mapping f: V (G)→{0, 1} such that f (v)∈ L (v) for each v∈ V (G), f− 1 (0) …

A graph is polar if its vertex set can be partitioned into A and B in such a way that A induces
a complete multipartite graph and B induces a disjoint union of cliques (ie, the complement …

A graph is polar if the vertex set can be partitioned into A and B in such a way that the
subgraph induced by A is a complete multipartite graph and the subgraph induced by B is a …

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