Mutual-Visibility Sets in Cartesian Products of Paths and Cycles

For a given graph G , the mutual-visibility problem asks for the largest set of vertices M ⊆ V ( G ) with the property that for any pair of vertices u , v ∈ M there exists a shortest u ,  v -path of G that does not pass through any other vertex in M . The mutual-visibility problem for Cartesian prod...

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Bibliographic Details
Published in:Resultate der Mathematik Vol. 79; no. 3; p. 116
Main Authors: Korže, Danilo, Vesel, Aleksander
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.05.2024
Springer Nature B.V
Subjects:
Apexes
Cartesian coordinates
Codes
Distributed processing
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Visibility
Mutual-visibility set
mutual-visibility number
05C12
68R10
Cartesian product
05C38
ISSN:1422-6383, 1420-9012
Online Access:Get full text
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Summary:For a given graph G , the mutual-visibility problem asks for the largest set of vertices M ⊆ V ( G ) with the property that for any pair of vertices u , v ∈ M there exists a shortest u ,  v -path of G that does not pass through any other vertex in M . The mutual-visibility problem for Cartesian products of a cycle and a path, as well as for Cartesian products of two cycles, is considered. Optimal solutions are provided for the majority of Cartesian products of a cycle and a path, while for the other family of graphs, the problem is completely solved.
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content type line 14
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-024-02139-x