Mutual-visibility Coloring of Graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910019635642368 |
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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 |