Mutual-visibility Coloring of Graphs

Fuente: arXiv
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Main Authors: Babu, Saneesh, Di Stefano, Gabriele, S, Aparna Lakshmanan
Format: Preprint
Published: 2025
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author Babu, Saneesh
Di Stefano, Gabriele
S, Aparna Lakshmanan
author_facet Babu, Saneesh
Di Stefano, Gabriele
S, Aparna Lakshmanan
contents The mutual-visibility chromatic number of a graph $G$ is the smallest number of colors needed to color the vertices of $G$ such that each color class is a mutual-visibility set. In this paper, we prove that determining the mutual-visibility chromatic number of a graph is NP-complete even when restricted to the class of graphs having diameter four and mutual-visibility chromatic number two. We further determine the exact value of the mutual-visibility chromatic number for glued binary trees and glued $t$-ary trees.
format Preprint
id arxiv_https___arxiv_org_abs_2512_12251
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Mutual-visibility Coloring of Graphs
Babu, Saneesh
Di Stefano, Gabriele
S, Aparna Lakshmanan
Combinatorics
05C15, 68Q17, 05C69
The mutual-visibility chromatic number of a graph $G$ is the smallest number of colors needed to color the vertices of $G$ such that each color class is a mutual-visibility set. In this paper, we prove that determining the mutual-visibility chromatic number of a graph is NP-complete even when restricted to the class of graphs having diameter four and mutual-visibility chromatic number two. We further determine the exact value of the mutual-visibility chromatic number for glued binary trees and glued $t$-ary trees.
title Mutual-visibility Coloring of Graphs
topic Combinatorics
05C15, 68Q17, 05C69
url https://arxiv.org/abs/2512.12251