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Co-2-plex vertex partitions

Author

Listed:
  • Benjamin McClosky
  • John D. Arellano

    (Rice University)

  • Illya V. Hicks

    (Rice University)

Abstract

This paper studies co-k-plex vertex partitions and more specifically co-2-plex vertex partitions. Co- $$k$$ k -plexes and $$k$$ k -plexes were first introduced in 1978 in the context of social network analysis. However, the study of co-k-plex vertex partitions or decomposing a graphs into degree bounded subgraphs can be at least dated back to the work of Lovasz (Studia Sci Math Hung 1:237–238, 1966). In this paper, we derive analogues for well-known results on the chromatic number, and present two algorithms for constructing co-2-plex vertex partitions. The first algorithm minimizes the number of partition classes while the second algorithm minimizes a weighted sum of the partition classes, where the weight of a partition class depends on the level of adjacency among its vertices.

Suggested Citation

  • Benjamin McClosky & John D. Arellano & Illya V. Hicks, 2015. "Co-2-plex vertex partitions," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 729-746, October.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:3:d:10.1007_s10878-013-9664-2
    DOI: 10.1007/s10878-013-9664-2
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    References listed on IDEAS

    as
    1. J. Randall Brown, 1972. "Chromatic Scheduling and the Chromatic Number Problem," Management Science, INFORMS, vol. 19(4-Part-1), pages 456-463, December.
    2. Benjamin McClosky & Illya V. Hicks, 2012. "Combinatorial algorithms for the maximum k-plex problem," Journal of Combinatorial Optimization, Springer, vol. 23(1), pages 29-49, January.
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