Co-2-plex vertex partitions

Benjamin McClosky (), John D. Arellano () and Illya V. Hicks ()
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John D. Arellano: Rice University
Illya V. Hicks: Rice University

Journal of Combinatorial Optimization, 2015, vol. 30, issue 3, No 20, 729-746

Abstract: 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.

Keywords: Co-2-plex coloring; Co-2-plex; 2-Plex; Independence systems (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-013-9664-2

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