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

Published 20 Mar 2014 in cs.DM and cs.CC | (1403.5248v3)

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.

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