## Continuation of a 3-coloring from a 7-face onto a plane graph without $$C_3$$.(Russian. English summary)Zbl 1077.05039

Let $$G$$ be a planar graph without 3-cycles. The authors investigate the following problem: When can a 3-coloring of the vertices of a face $$F$$ of $$G$$ be extended to a 3-coloring of the whole graph $$G$$? In previous papers they studied the cases in which $$F$$ is a 5-face [V. A. Aksenov, Diskret. Analiz, Novosibirsk 26, 3-19 (1974; Zbl 0308.05107)] or a 6-face [V. A. Aksenov, O. V. Borodin, and A. N. Glebov, Diskretn. Anal. Issled. Oper., Ser. 1 10, 3–11 (2003; Zbl 1047.05014)]. In the present paper, necessary and sufficient conditions are obtained for the extensibility of a 3-coloring of the vertices of a 7-face $$F$$ of a graph $$G$$ without 3-cycles to the whole graph.

### MSC:

 05C15 Coloring of graphs and hypergraphs

### Citations:

Zbl 0308.05107; Zbl 1047.05014
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