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arXiv · 1512.02207

The complexity of partitioning into disjoint cliques and a triangle-free graph

Marin Bougeret·Pascal Ochem
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Abstract

Motivated by Chudnovsky's structure theorem of bull-free graphs, Abu-Khzam, Feghali, and M\"uller have recently proved that deciding if a graph has a vertex partition into disjoint cliques and a triangle-free graph is NP-complete for five graph classes. The problem is trivial for the intersection of these five classes. We prove that the problem is NP-complete for the intersection of two subsets of size four among the five classes. We also show NP-completeness for other small classes, such as graphs with maximum degree 4 and line graphs.

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Marin Bougeret, Pascal Ochem. 2015-12-07. The complexity of partitioning into disjoint cliques and a triangle-free graph. https://arxiv.org/abs/1512.02207

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