Mohar's Kempe-equivalence conjecture for edge-colourings

Let GG be a simple graph. Two kk-edge-colourings are Kempe-equivalent if one can be reached from the other through a series of Kempe changes using colours from {1,,k}\{1,\ldots,k\}. Mohar's conjecture. All (Δ(G)+2)(\Delta(G)+2)-edge-colourings of GG 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.

Sources & referencesView supporting material

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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