Abstract
The entire chromatic number χ vef (G) of a plane graph G is the minimal number of colors needed for coloring vertices, edges and faces of G such that no two adjacent or incident elements are of the same color. Let G be a series-parallel plane graph, that is, a plane graph which contains no subgraphs homeomorphic to K 4. It is proved in this paper that χ vef (G) ≤ max{8, Δ(G) + 2} and χ vef (G) =Δ+1 if G is 2-connected and Δ(G) ≥ 6.
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Supported by the National Natural Science Foundation of China (No.10471078) and the Doctoral Foundation of the Education Committee of China (No. 2004042204)
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Wu, Jl., Wu, Yl. The Entire Coloring of Series-Parallel Graphs. Acta Mathematicae Applicatae Sinica, English Series 21, 61–66 (2005). https://doi.org/10.1007/s10255-005-0215-1
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DOI: https://doi.org/10.1007/s10255-005-0215-1