Third case of the Cyclic Coloring Conjecture
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 6colorable. We prove the case D=6 of the conjecture.
 Publication:

arXiv eprints
 Pub Date:
 January 2015
 arXiv:
 arXiv:1501.06624
 Bibcode:
 2015arXiv150106624H
 Keywords:

 Mathematics  Combinatorics