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Simultaneous coloring of edges and faces of plane graphs. (English) Zbl 0807.05029
The edge-and-face chromatic number $$\chi_{\text{ef}}(G)$$ of a plane graph $$G$$ is the least number of colors required to color the edges and faces of $$G$$ such that every two adjacent or incident of them receive different colors. It is proved that if $$G$$ is a plane graph with maximum degree at least 10 then $$\chi_{\text{ef}}(G)\leq \Delta(G)+1$$, the bound being sharp. The proof is based on some new generalizations of Kotzig’s Theorem on the minimal weight of edges in plane graphs. It is also proved that if $$G$$ is a plane graph without separating triangles and $$\Delta(G)\leq 7$$ then $$\chi_{\text{ef}}(G)\leq 10$$.
Reviewer: M.Frick (Pretoria)

##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C10 Planar graphs; geometric and topological aspects of graph theory
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