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List edge and list total coloring of 1-planar graphs. (English) Zbl 1254.05050
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 each 1-planar graph with maximum degree \(\Delta\) is (\(\Delta+1\))-edge-choosable and (\(\Delta+2\))-total-choosable if \(\Delta \geqslant 16\), and is \(\Delta\)-edge-choosable and (\(\Delta+1\))-total-choosable if \(\Delta \geqslant 21\). The second conclusion confirms the list coloring conjecture for the class of 1-planar graphs with large maximum degree.

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
05C15 Coloring of graphs and hypergraphs
05C07 Vertex degrees
05C35 Extremal problems in graph theory
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