Partitioning a Graph into Disjoint Cliques and a Trianglefree Graph
Abstract
A graph $G = (V, E)$ is \emph{partitionable} if there exists a partition $\{A, B\}$ of $V$ such that $A$ induces a disjoint union of cliques and $B$ induces a trianglefree graph. In this paper we investigate the computational complexity of deciding whether a graph is partitionable. The problem is known to be $\NP$complete on arbitrary graphs. Here it is proved that if a graph $G$ is bullfree, planar, perfect, $K_4$free or does not contain certain holes then deciding whether $G$ is partitionable is $\NP$complete. This answers an open question posed by Thomass{é}, Trotignon and Vuškovi{ć}. In contrast a finite list of forbidden induced subgraphs is given for partitionable cographs.
 Publication:

arXiv eprints
 Pub Date:
 March 2014
 arXiv:
 arXiv:1403.5961
 Bibcode:
 2014arXiv1403.5961A
 Keywords:

 Computer Science  Computational Complexity;
 Computer Science  Discrete Mathematics;
 Mathematics  Combinatorics;
 68R10
 EPrint:
 20 pages