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doi:10.1016/0012-365X(92)90647-X 
Copyright © 1992 Published by Elsevier Science B.V. All rights reserved.
Cyclic coloring of plane graphs
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Oleg V. Borodin
Received 10 October 1990;
revised 23 October 1991.
Available online 3 April 2002.
Abstract
Let G be a plane graph, and let χk(G) be the minimum number of colors to color the vertices of G so that every two of them which lie in the boundary of the same face of the size at most k, receive different colors. In 1966, Ore and Plummer proved that χk(G)
2k for any k
3. It is also known that χ3(G)4 (Appel and Haken, 1976) and χ4(G)6 (Borodin, 1984). The result in the present paper is: χ5(G)9, χ6(G)11, χ7(G)12, and χk(G)2k − 3 if k8.
