Vizing's edge-recoloring conjecture holds
Combinatorics
2023-02-28 v1 Discrete Mathematics
Abstract
In 1964 Vizing proved that starting from any k-edge-coloring of a graph G one can reach, using only Kempe swaps, a ( + 1)-edge-coloring of G where is the maximum degree of G. One year later he conjectured that one can also reach a -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.
Cite
@article{arxiv.2302.12914,
title = {Vizing's edge-recoloring conjecture holds},
author = {Jonathan Narboni},
journal= {arXiv preprint arXiv:2302.12914},
year = {2023}
}