Partition into cliques for cubic graphs: Planar case, complexity and approximation

Given a graph G = (V, E) and a positive integer k, the PARTITION INTO CLIQUES (PIC) decision problem consists of deciding whether there exists a partition of V into k disjoint subsets V1, V2, . . . , Vk such that the subgraph induced by each part Vi is a complete subgraph (clique) of G. In this paper, we establish both the NP-completeness of PIC for planar cubic graphs and the Max SNP-hardness of PIC for cubic graphs. We present a deterministic polynomial time 5 4 -approximation algorithm for finding clique partitions in maximum degree three graphs. c 2007 Elsevier B.V. All rights reserved.

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Márcia R. Cerioli, L. Faria, T. O. Ferreira, Carlos A. J. Martinhon, Fábio Protti, Bruce A. Reed
• Keywords: Clique, Cubic Graphs, DAM 2008, Positive Integer