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

نویسندگان

  • Márcia R. Cerioli
  • Luérbio Faria
  • Talita O. Ferreira
  • Carlos Alberto de Jesus Martinhon
  • Fábio Protti
  • Bruce A. Reed
چکیده

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 4 -approximation algorithm for finding clique partitions in maximum degree three graphs. c © 2007 Elsevier B.V. All rights reserved.

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عنوان ژورنال:
  • Discrete Applied Mathematics

دوره 156  شماره 

صفحات  -

تاریخ انتشار 2008