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A note on total colorings of planar graphs without 4-cycles. (English) Zbl 1056.05067
Summary: Let $$G$$ be a 2-connected planar graph with maximum degree $$\Delta$$ such that $$G$$ has no cycle of length from 4 to $$k$$, where $$k\geq 4$$. Then the total chromatic number of $$G$$ is $$\Delta+1$$ if $$(\Delta,k)\in\{(7,4),(6,5), (5,7), (4,14)\}$$.

##### MSC:
 05C15 Coloring of graphs and hypergraphs
##### Keywords:
total coloring; planar graph; list coloring; girth; chromatic number
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