NP-hardness results for partitioning graphs into disjoint cliques and a triangle-free subgraph
Carl Feghali, Faisal N. Abu-Khzam, Haiko Müller · arXiv (Cornell University) · 2014
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.