Edge-Face Total Chromatic Number of Halin Graphs
β Scribed by Chan, W. H.; Lam, Peter C. B.; Shiu, W. C.
- Book ID
- 118197679
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2009
- Tongue
- English
- Weight
- 513 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0895-4801
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π SIMILAR VOLUMES
In this paper, we shall first prove that for a Halin graph G, 4 Β°xT (G) Β°6, where x T (G) is the vertex-face total chromatic number of G. Second, we shall establish a sufficient condition for a Halin graph to have a vertex-face total chromatic number of 6. Finally, we shall give a necessary and suff
## Abstract Given a simple plane graph __G__, an edgeβface __k__βcoloring of __G__ is a function Ο : __E__(__G__) βͺ __F__(G)βββ {1,β¦,__k__} such that, for any two adjacent or incident elements __a__, __b__ β __E__(__G__) βͺ __F__(__G__), Ο(__a__)ββ βΟ(__b__). Let Ο~e~(__G__), Ο~ef~(__G__), and Ξ(__G_
In this paper, we prove that XT(G) = 5 for any Halin graph G with A(G) = 4, where A(G) and XT(G) denote the maximal degree and the total chromatic number of G, respectively.