Covering graphs with convex sets and partitioning graphs into convex sets

Abstract

We present some complexity results concerning the problems of covering a graph with $p$ convex sets and of partitioning a graph into $p$ convex sets. The following convexities are considered: digital convexity, monophonic convexity, $P_3$-convexity, and $P_3^{\ast }$-convexity.

10 pages