Convex graph covers

Abstract

We study some properties of minimum convex covers and minimum convex partitions of simple graphs. We establish existence of graphs with fixed number of minimum convex covers and minimum convex partitions. It is known that convex $p$-cover problem is NP-complete for $p\geq3$ [5]. We prove that this problem is NP-complete in the case $p=2$. Also, we study covers and partitions of graphs when respective sets are nontrivial convex.

Keywords

• Convexity
• graphs
• convex covers
• convex partitions