Mohar's Kempe-equivalence conjecture for edge-colourings

About 11 years old · traced to

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.

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.

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.