Geodesic
On Edge Colorings of 1-Planar Graphs without 5-Cycles with Two Chords
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 301-312

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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 with maximum degree ∆ ≥ 8 is edge-colorable with ∆ colors if each of its 5-cycles contains at most one chord.
Keywords: 1-planar graphs, edge coloring, discharging method 
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     title = {On {Edge} {Colorings} of {1-Planar} {Graphs} without {5-Cycles} with {Two} {Chords}},
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Sun, Lin; Wu, Jianliang. On Edge Colorings of 1-Planar Graphs without 5-Cycles with Two Chords. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 301-312. http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a0/