An upper bound on the number of edges of edge-coloring critical graphs with high maximum degree

摘要

In this paper, we prove that any edge-coloring critical graph G with maximum degree Δ ≥ (11 + (49-24ε)~(1/2))/2, where ε ≤ 1, has the size at least 3(|V(G)| - ε) + 1 if δ ≤ 7 or if δ ≥ 8 and |V(G)| > 2Δ - δ - 4 - (Δ + 6)/(δ - 6), where δ is the minimum degree of G. It generalizes a result of Sanders and Zhao.