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 ...

Let G be a connected graph. We say that a set S ⊆ X(G) is convex in G if, for any two vertices x, y ∈ S, all vertices of every shortest path between x and y are in S. If 3 ≤ |S| ≤ |X(G)| − 1, then S is a nontrivial set. ...

A vertex set S of a graph G is convex if all vertices of every shortest path between two of its vertices are in S. We say that G has a convex p-cover if X (G)can be overed by p convex sets. The convex cover number of G Is ...

In this paper we present further studies of convex covers and convex partitions of graphs. Let G be a finite simple graph. A set of vertices S of G is convex if all vertices lying on a shortest path between any ...