On Vizing's edge colouring question

Aur\'elie Lagoutte; Jonathan Narboni; Marthe Bonamy; Oscar Defrain; Tereza Klimo\v{s}ov\'a

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On Vizing's edge colouring question

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arxiv 2107.07900 v1 pith:WHIGMHRL submitted 2021-07-16 math.CO cs.DM

Marthe Bonamy , Oscar Defrain , Tereza Klimošová , Aurélie Lagoutte , Jonathan Narboni This is my paper · ORCID

classification math.COcs.DM

keywords colouringedgequestionvizingaffirmativeansweraskedchanges

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Soon after his 1964 seminal paper on edge colouring, Vizing asked the following question: can an optimal edge colouring be reached from any given proper edge colouring through a series of Kempe changes? We answer this question in the affirmative for triangle-free graphs.

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