摘要
The entire chromatic number χ_(vef) (G) of a plane graph G is the minimalnumber of colors needed for coloring vertices, edges and faces of G such that no two adjacent orincident elements are of the same color. Let G be a series-parallel plane graph, that is, a planegraph 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.
The entire chromatic number χ_(vef) (G) of a plane graph G is the minimalnumber of colors needed for coloring vertices, edges and faces of G such that no two adjacent orincident elements are of the same color. Let G be a series-parallel plane graph, that is, a planegraph 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.
基金
Supported by the National Natural Science Foundation of China (No. 10471078)
the Doctoral Foundation of the Education Committee of China (No. 2004042204)
