Bojan Mohar is on leave from IMFM 8 FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia.
Kempe Equivalence of Edge-Colorings in Subcubic and Subquartic Graphs†
Article first published online: 26 APR 2011
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 70, Issue 2, pages 226–239, June 2012
How to Cite
McDonald, J., Mohar, B. and Scheide, D. (2012), Kempe Equivalence of Edge-Colorings in Subcubic and Subquartic Graphs. J. Graph Theory, 70: 226–239. doi: 10.1002/jgt.20613
- Issue published online: 25 APR 2012
- Article first published online: 26 APR 2011
- Manuscript Revised: 28 FEB 2011
- Manuscript Received: 26 MAY 2010
- Kempe changes
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