Discussiones Mathematicae Graph Theory (May 2019)

On Edge Colorings of 1-Planar Graphs without 5-Cycles with Two Chords

  • Sun Lin,
  • Wu Jianliang

DOI
https://doi.org/10.7151/dmgt.2072
Journal volume & issue
Vol. 39, no. 2
pp. 301 – 312

Abstract

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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.

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