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Solution of Ringel’s problems concerning the vertex-faced coloring of planar graphs and the coloring of 1-planar graphs. (Russian) Zbl 0565.05027
The author proves that the coupled colouring number of any plane graph does not exceed 6, settling thereby a conjecture of G. Ringel [Ein Sechsfarbenproblem auf der Kugel, Abh. Math. Semin. Univ. Hamb., 29, 107- 117 (1965; Zbl 0132.207)]. For a related result on graphs embedded on the projective plane, see H. Schumacher [Abh. Math. Semin. Univ. Hamb. 54, 5-14 (1984; Zbl 0557.05037)].
Reviewer: J.Širáň

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