Mohar's Kempe-equivalence conjecture for edge-colourings
Let be a simple graph. Two -edge-colourings are Kempe-equivalent if one can be reached from the other through a series of Kempe changes using colours from . Mohar's conjecture. All -edge-colourings of are Kempe-equivalent. This conjecture would strengthen Vizing's question, which asks whether every edge-colouring using more than the chromatic index can be reduced to an optimal colouring by Kempe changes. Its status is not resolved in the supplied source context.
References
Primary source
Marthe Bonamy, Oscar Defrain, Tereza Klimošová, Aurélie Lagoutte and Jonathan Narboni, “On Vizing's edge colouring question”, arXiv:2107.07900 (2021).
Additional references
3 papers in this index state this conjecture (2015–2021). The statement above is taken from the most recent of them; the others are arXiv:2101.04065, arXiv:1503.03430.
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