Third case of the Cyclic Coloring Conjecture
Combinatorics
2016-02-08 v4
Abstract
The Cyclic Coloring Conjecture asserts that the vertices of every plane graph with maximum face size D can be colored using at most 3D/2 colors in such a way that no face is incident with two vertices of the same color. The Cyclic Coloring Conjecture has been proven only for two values of D: the case D=3 is equivalent to the Four Color Theorem and the case D=4 is equivalent to Borodin's Six Color Theorem, which says that every graph that can be drawn in the plane with each edge crossed by at most one other edge is 6-colorable. We prove the case D=6 of the conjecture.
Cite
@article{arxiv.1501.06624,
title = {Third case of the Cyclic Coloring Conjecture},
author = {Michael Hebdige and Daniel Kral},
journal= {arXiv preprint arXiv:1501.06624},
year = {2016}
}