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 \(S \subseteq V(G)\) 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.
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Partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil, Grant number 305404/2020-2.
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Dourado, M.C. Computing the hull number in toll convexity. Ann Oper Res 315, 121–140 (2022). https://doi.org/10.1007/s10479-022-04694-4
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DOI: https://doi.org/10.1007/s10479-022-04694-4