Edge colourings of embedded graphs without 4-cycles or chordal-4-cycles
Jianfeng Hou, Bin Liu, Guizhen Liu, Jihui Wang · International Journal of Computer Mathematics · 2010
Let G be a simple graph embedded in a surface Σ of Euler characteristic χ(Σ)≥0, and let χ′(G) and Δ denote the chromatic index and the maximum degree of G, respectively. The paper shows that χ′(G)=Δ if Δ≥6 and G does not contain chordal-4-cycles or Δ≥5 and G does not contain 4-cycles.