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

Authors:
M. R. Cerioli;L. Faria;T. O. Ferreira;C. A. J. Martinhon;F. Protti;B. Reed
Affiliations:
IM - UFRJ, Rio de Janeiro, Brazil and COPPE - UFRJ, Rio de Janeiro, Brazil;DMAT, FFP - UERJ, Rio de Janeiro, Brazil;COPPE - UFRJ, Rio de Janeiro, Brazil;IC - UFF, Rio de Janeiro, Brazil;IM - UFRJ, Rio de Janeiro, Brazil and NCE - UFRJ, Caixa Postal 2324, 20001-970, Rio de Janeiro, Rj, Brazil;School of Computer Science, McGill University, Montreal, Quebec, Canada
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

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 V"1,V"2,...,V"k such that the subgraph induced by each part V"i 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 54-approximation algorithm for finding clique partitions in maximum degree three graphs.