This paper is focused on some aspects of undirected graphs covering, in particular convex sets problem (CCS) and partitioning undirected graph into convex sets problem (PCS). We prove theorems regarding existence of graphs with fxed number of convex sets which serve as solutions to CCS and PCS problems.
(Academy of Sciences of Moldova, 2015) Buzatu, Radu; Cataranciuc, Sergiu
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.
