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On the vertex face total chromatic number of planar graphs

✍ Scribed by Weifan, Wang; Jiazhuang, Liu

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 471 KB
Volume: 22
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199605)22:1<29::aid-jgt5>3.0.co;2-n

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✦ Synopsis

Let G be a planar graph. The vertex face total chromatic number ,y13(G) of G is the least number of colors assigned to V(G) U F(G) such that no adjacent or incident elements receive the same color. The main results of this paper are as follows: (1) We give the vertex face total chromatic number for all outerplanar graphs and modulus 3-regular maximal planar graphs. (2) We prove that if G is a maximal planar graph or a lower degree planar graph, i.e., A(G) 5 3, then ,y13(G) 5 6. 0 1996 John Wiley & Sons, Inc.

Definition 1.1. A proper vertex face total coloring of a planar graph G, which is called a VFcoloring of G in short, is an assignment of colors to SvF(G) such that no adjacent or incident elements receive the same color. If G has a proper VF-coloring using k colors then G is called

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