ON NONTRIVIAL COVERS AND PARTITIONS OF GRAPHS BY CONVEX SETS

Abstract

In this paper we prove that it is NP-complete to decide whet- her a graph can be partitioned into nontrivial convex sets. We show that it can be verified in polynomial time whether a graph can be covered by nontrivial convex sets. Also, we propose a re- cursive formula that establishes the maximum nontrivial convex cover number of a tree.