English

Note on robust coloring of planar graphs

Combinatorics 2024-12-24 v2

Abstract

We consider the robust chromatic number χ1(G)\chi_1(G) of planar graphs GG and show that there exists an infinite family of planar graphs GG with χ1(G)=3\chi_1(G) = 3, thus solving a recent problem of Bacs\'{o}~et~al. (The robust chromatic number of graphs, Graphs Combin. 40 (2024), #89).

Keywords

Cite

@article{arxiv.2401.08324,
  title  = {Note on robust coloring of planar graphs},
  author = {František Kardoš and Borut Lužar and Roman Soták},
  journal= {arXiv preprint arXiv:2401.08324},
  year   = {2024}
}
R2 v1 2026-06-28T14:17:58.760Z