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Computing the hull number in toll convexity

Author

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  • Mitre C. Dourado

    (Universidade Federal do Rio de Janeiro)

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.

Suggested Citation

  • Mitre C. Dourado, 2022. "Computing the hull number in toll convexity," Annals of Operations Research, Springer, vol. 315(1), pages 121-140, August.
    • Handle: RePEc:spr:annopr:v:315:y:2022:i:1:d:10.1007_s10479-022-04694-4
    DOI: 10.1007/s10479-022-04694-4
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