Edge colorings of graphs embeddable in a surface of low genus Original Research Article

In this paper, by using the Discharging Method, we show that any graph with maximum degree Δ ⩾ 8 that is embeddable in a surface Σ of characteristic χ(Σ) ⩾ 0 is class one and any graph with maximum degree Δ ⩾ 9 that is embeddable in a surface Σ of characteristic χ(Σ) = − 1 is class one. For surfaces of characteristic 0 or −1, these results improve earlier results of Melʹnikov.