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The nontrivial convex 2-cover problem of a simple graph is studied. We establish the existence of a convex (2, nt)-cover in dependency of existing convex (2, t)-covers. We prove that it is NP-complete to decide whether a graph that has convex (2, t)-covers also has a convex (2, nt)-cover. In addition, we identify some classes of graphs for which there exists a convex (2, nt)-cover.
Keywords and phrases: convexity, convex covers, simplicial vertex, NP-completeness, convex partition.
2010 Mathematics Subject Classification. 05C35, 05C85.
