In 1964 Vizing proved that starting from any k-edge-coloring of a graph G one can reach, using only Kempe swaps, a ($\Delta$ + 1)-edge-coloring of G where $\Delta$ is the maximum degree of G. One year later he conjectured that one can also reach a $\Delta$-edge-coloring of G if there exists one. Bonamy et. al proved that the conjecture is true for the case of triangle-free graphs. In this paper we prove the conjecture for all graphs.

翻译：1964年，Vizing证明从图G的任意k边染色出发，通过仅使用Kempe交换，总能得到G的(Δ+1)-边染色，其中Δ为图G的最大度。次年他猜想：若图G存在Δ-边染色，则同样可通过Kempe交换得到该染色。Bonamy等人证明了该猜想在三角形自由图中成立。本文证明了该猜想对所有图均成立。