On 2-distance 16-coloring of planar graphs with maximum degree at most five
Combinatorics
2025-08-21 v3
Abstract
A vertex coloring of a graph G is called a 2-distance coloring if any two vertices at a distance at most 2 from each other receive different colors. Suppose that G is a planar graph with a maximum degree at most 5. We prove that G admits a 2-distance 16 coloring, which improves the result given by Hou et al. (Graphs and Combinatorics 39:20, 2023).
Cite
@article{arxiv.2310.15899,
title = {On 2-distance 16-coloring of planar graphs with maximum degree at most five},
author = {Zakir Deniz},
journal= {arXiv preprint arXiv:2310.15899},
year = {2025}
}
Comments
In this revised version, Lemma 2.22 has been updated to address a few corrected errors