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的任何K-对开色开始,只能使用Kempe交换,可以达到G($\Delta$+1)-对开色,其中$\Delta$是G的最高等级。 一年后,他推测,如果有的话,也可以达到G($\Delta$-对开色)。 Bonamy等人证明,对于没有三角形的图表来说,推测是真实的。在本文中,我们证明了所有图表的假设。</s>