Mutual-visibility Coloring of Graphs
Saneesh Babu, Gabriele Di Stefano, Aparna Lakshmanan S

TL;DR
This paper investigates the mutual-visibility coloring problem in graphs, proving its computational complexity and providing exact solutions for specific tree structures.
Contribution
It establishes NP-completeness of the mutual-visibility chromatic number problem and computes exact values for glued binary and t-ary trees.
Findings
Mutual-visibility chromatic number determination is NP-complete.
Exact values are found for glued binary trees.
Exact values are found for glued t-ary trees.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Computational Geometry and Mesh Generation
