Mutual-visibility Coloring of Graphs
Combinatorics
2026-02-13 v2
Abstract
The mutual-visibility chromatic number of a graph is the smallest number of colors needed to color the vertices of 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 -ary trees.
Cite
@article{arxiv.2512.12251,
title = {Mutual-visibility Coloring of Graphs},
author = {Saneesh Babu and Gabriele Di Stefano and Aparna Lakshmanan S},
journal= {arXiv preprint arXiv:2512.12251},
year = {2026}
}