English

Cyclic Coloring of Plane Graphs with Maximum Face Size 16 and 17

Combinatorics 2020-12-10 v4

Abstract

Plummer and Toft conjectured in 1987 that the vertices of every 3-connected plane graph with maximum face size D can be colored using at most D+2 colors in such a way that no face is incident with two vertices of the same color. The conjecture has been proven for D=3, D=4 and D>=18. We prove the conjecture for D=16 and D=17.

Keywords

Cite

@article{arxiv.1603.06722,
  title  = {Cyclic Coloring of Plane Graphs with Maximum Face Size 16 and 17},
  author = {Zdenek Dvorak and Michael Hebdige and Filip Hlasek and Daniel Kral and Jonathan Noel},
  journal= {arXiv preprint arXiv:1603.06722},
  year   = {2020}
}

Comments

Accepted to the European Journal of Combinatorics