Mutual-visibility in distance-hereditary graphs: a linear-time algorithm

The concept of mutual-visibility in graphs has been recently introduced. If X is a subset of vertices of a graph G, then vertices u and v are X-visible if there exists a shortest u, v-path P such that V(P) ∩ X⊆ {u, v}. If every two vertices from X are X-visible, then X is a mutual-visibility set. Th...

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Bibliographic Details
Published in:Procedia computer science Vol. 223; pp. 104 - 111
Main Authors: Cicerone, Serafino, Stefano, Gabriele Di
Format: Journal Article
Language:English
Published: Elsevier B.V 2023
Subjects:
Computational complexity
Graph algorithm
Graph classes
Graph invariant
Mutual visibility
Mutual visibility
Graph classes
Graph invariant
Computational complexity
Graph algorithm
ISSN:1877-0509, 1877-0509
Online Access:Get full text
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Summary:The concept of mutual-visibility in graphs has been recently introduced. If X is a subset of vertices of a graph G, then vertices u and v are X-visible if there exists a shortest u, v-path P such that V(P) ∩ X⊆ {u, v}. If every two vertices from X are X-visible, then X is a mutual-visibility set. The mutual-visibility number of G is the cardinality of a largest mutual-visibility set of G. It is known that computing the mutual-visibility number of a graph is NP-complete, whereas it has been shown that there are exact formulas for special graph classes like paths, cycles, blocks, cographs, and grids. In this paper, we study the mutual-visibility in distance-hereditary graphs and show that the mutual-visibility number can be computed in linear time for this class.
ISSN:1877-0509
1877-0509
DOI:10.1016/j.procs.2023.08.219