Computing the hull number in toll convexity

Mitre C. Dourado ()
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Mitre C. Dourado: Universidade Federal do Rio de Janeiro

Annals of Operations Research, 2022, vol. 315, issue 1, No 6, 140 pages

Abstract: Abstract A tolled walk W between vertices u and v in a graph G is a walk in which u is adjacent only to the second vertex of W and v is adjacent only to the second-to-last vertex of W. A set $$S \subseteq V(G)$$ S ⊆ V ( G ) is toll convex if the vertices contained in any tolled walk between two vertices of S are contained in S. The toll convex hull of S is the minimum toll convex set containing S. The toll hull number of G is the minimum cardinality of a set whose toll convex hull is V(G). The main contribution of this work is a polynomial-time algorithm for computing the toll hull number of a general graph.

Keywords: Extreme vertex; Hull number; Minimum toll hull sets; Toll convexity; 05C85 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-022-04694-4

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