English

2-distance 4-coloring of planar subcubic graphs with girth at least 21

Combinatorics 2025-03-12 v4 Discrete Mathematics

Abstract

A 22-distance kk-coloring of a graph is a proper vertex kk-coloring where vertices at distance at most 2 cannot share the same color. We prove the existence of a 22-distance 44-coloring for planar subcubic graphs with girth at least 21. We also show a construction of a planar subcubic graph of girth 11 that is not 22-distance 44-colorable.

Keywords

Cite

@article{arxiv.2106.03587,
  title  = {2-distance 4-coloring of planar subcubic graphs with girth at least 21},
  author = {Hoang La and Mickael Montassier},
  journal= {arXiv preprint arXiv:2106.03587},
  year   = {2025}
}

Comments

21 pages, 14 figures