The complexity of partitioning into disjoint cliques and a triangle-free graph
Discrete Mathematics
2015-12-08 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.1512.02207,
title = {The complexity of partitioning into disjoint cliques and a triangle-free graph},
author = {Marin Bougeret and Pascal Ochem},
journal= {arXiv preprint arXiv:1512.02207},
year = {2015}
}