Edge coloring of graphs with small average degrees Original Research Article

Let G be a simple graph with average degree d̄ and maximum degree Δ. It is proved, in this paper that G is not critical if d̄⩽6 and Δ⩾8, or d̄⩽203 and Δ⩾9. This result generalizes earlier results of Vizing (Metody Diskret. Analiz. 5 (1965) 9), Melʹnikov (Mat. Zametki 7 (1970) 671) and Hind and Zhao (Discrete Math. 190 (1998) 107) and Yan and Zhao (Graphs Combin. 16 (2) (2000) 245). It also improves a result by Fiorini (Math. Proc. Cambridge Philos. Soc. 77 (1975) 475) on the number of edges of critical graphs for certain Δ.