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On total colorings of 1-planar graphs. (English) Zbl 1317.05066
Summary: A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we confirm the total-coloring conjecture for 1-planar graphs with maximum degree at least 13.

##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C10 Planar graphs; geometric and topological aspects of graph theory 05C62 Graph representations (geometric and intersection representations, etc.)
##### Keywords:
1-planar graph; total coloring; discharging method
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##### References:
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