摘要
A total k-coloring of a graph G is a coloring of V(G) ∪ E(G) using k colors such that no two adjacent or incident elements receive the same color.The total chromatic number χ〃(G) is the smallest integer k such that G has a total k-coloring.In this paper,it is proved that the total chromatic number of any graph G embedded in a surface Σ of Euler characteristic χ(Σ)≥0 is Δ(G) + 1 if Δ(G)≥10,where Δ(G) denotes the maximum degree of G.
A total k-coloring of a graph G is a coloring of V(G) ∪ E(G) using k colors such that no two adjacent or incident elements receive the same color.The total chromatic number χ〃(G) is the smallest integer k such that G has a total k-coloring.In this paper,it is proved that the total chromatic number of any graph G embedded in a surface Σ of Euler characteristic χ(Σ)≥0 is Δ(G) + 1 if Δ(G)≥10,where Δ(G) denotes the maximum degree of G.
基金
supported by the Research Foundation for Doctor Programme (Grant No.200804220001)
National Natural Science Foundation of China (Grant Nos.10871119,10971121,10901097)
