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On edge colorings of 1-planar graphs without adjacent triangles. (English) Zbl 1239.05078
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, it is proved that every 1-planar graph without adjacent triangles and with maximum degree $$\Delta \geqslant 8$$ can be edge-colored with $$\Delta$$ colors.

##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C07 Vertex degrees 05C10 Planar graphs; geometric and topological aspects of graph theory
##### Keywords:
1-planar graphs; edge coloring; combinatorial problems
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##### References:
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