Kempe equivalence of edge-colourings in subcubic and subquartic graphs

Details Kempe equivalence of edge-colourings in subcubic and subquartic graphs Kempe equivalence of edge-colourings in subcubic and subquartic graphs

2010-05-13

arxiv.org/abs/1005.2248v2

Mathematics

Combinatorics

15 pages, 7 figures

Scientific paper

It is proved that all 4-edge-colourings of a (sub)cubic graph are Kempe equivalent. This resolves a conjecture of the second author. In fact, it is found that the maximum degree Delta=3 is a threshold for Kempe equivalence of (Delta+1)-edge-colourings, as such an equivalence does not hold in general when Delta=4. One extra colour allows a similar result in this latter case however, namely, when Delta<=4 it is shown that all (Delta+2)-edge-colourings are Kempe equivalent.

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