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

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

2009-12-24

arxiv.org/abs/0912.4770v2

Mathematics

Combinatorics

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

Scientific paper

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

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