English

Every plane graph of maximum degree 8 has an edge-face 9-colouring

Combinatorics 2012-07-18 v2

Abstract

An edge-face colouring of a plane graph with edge set EE and face set FF is a colouring of the elements of EFE \cup F such that adjacent or incident elements receive different colours. Borodin proved that every plane graph of maximum degree Δ10\Delta\ge10 can be edge-face coloured with Δ+1\Delta+1 colours. Borodin's bound was recently extended to the case where Δ=9\Delta=9. In this paper, we extend it to the case Δ=8\Delta=8.

Keywords

Cite

@article{arxiv.0912.4770,
  title  = {Every plane graph of maximum degree 8 has an edge-face 9-colouring},
  author = {Ross J. Kang and Jean-Sébastien Sereni and Matěj Stehlík},
  journal= {arXiv preprint arXiv:0912.4770},
  year   = {2012}
}

Comments

29 pages, 1 figure; v2 corrects a contraction error in v1; to appear in SIDMA