Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4949752 | Discrete Applied Mathematics | 2017 | 8 Pages |
Abstract
Motivated by Chudnovsky's structure theorem of bull-free graphs, Abu-Khzam, Feghali, and Müller 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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Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Marin Bougeret, Pascal Ochem,