English

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).

Keywords

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