2 research outputs found
On Edge Colorings of 1-Planar Graphs without 5-Cycles with Two Chords
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 β β₯ 8 is edge-colorable with β colors if each of its 5-cycles contains at most one chord