Co-2-plex vertex partitions

This paper studies co-k-plex vertex partitions and more specifically co-2-plex vertex partitions. Co-k-plexes and k-plexes were first introduced in 1978 in the context of social network analysis. However, the study of co-k-plex vertex partitions, or the decomposition of graphs into degree bounded subgraphs, dates back at least to the work of Lovasz in 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. 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.