Computer Science Journal of Moldova (May 2018)
On Nontrivial Covers and Partitions of Graphs by Convex Sets
Abstract
In this paper we prove that it is NP-complete to decide whether 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 recursive formula that establishes the maximum nontrivial convex cover number of a tree.