Abstract
Given a graph G, a set S⊆V(G) is Δ-convex if there is no vertex u∈V(G)∖S forming a triangle with two vertices of S. The Δ-convex hull of S is the minimum Δ-convex set containing S. The Δ-hull number of a graph G is the cardinality of a minimum set such that its Δ-convex hull is V(G). We show that the problem of deciding whether the Δ-hull number of a general graph is at most k is an NP-complete problem and present polynomial-time algorithms for computing the Δ-hull number of some graph classes including chordal graphs, dually chordal graphs, and cographs.
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