NP-hardness results for partitioning graphs into disjoint cliques and a triangle-free subgraph

Abstract

This paper investigates the computational complexity of deciding whether the vertices of a graph can be partitioned into a disjoint union of cliques and a triangle-free subgraph. This problem is known to be $\NP$-complete on arbitrary graphs. We show that this problem remains $\NP$-complete even when restricted to planar graphs and perfect graphs.

10 pages, 4 figures. The results in this paper can now be found, including further results, in our submission entitled "On the Complexity of Partitioning a Graph into Disjoint Cliques and a Triangle-free Subgraph", arXiv:1403.5961