SEARCH

SEARCH BY CITATION

Keywords:

  • edge–coloring;
  • Kempe changes

Abstract

It is proved that all 4-edge-colorings 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 Δ = 3 is a threshold for Kempe equivalence of (Δ+1)-edge-colorings, as such an equivalence does not hold in general when Δ = 4. One extra color allows a similar result in this latter case; however, namely, when Δ≤4 it is shown that all (Δ+2)-edge-colorings are Kempe equivalent. © 2011 Wiley Periodicals, Inc. J Graph Theory