Kempe equivalent list edge-colorings of planar graphs

Abstract

For a list assignment L and an L-coloring φ, a Kempe swap in φ is L-valid if it yields another L-coloring. Two L-colorings are L-equivalent if we can form one from another by a sequence of L-valid Kempe swaps. And a graph G is L-swappable if every two of its L-colorings are L-equivalent. We consider L-swappability of line graphs of planar graphs with large maximum degree. Let G be a planar graph with Δ(G)≥9 and let H be the line graph of G. If L is a (Δ(G)+1)-assignment to H, then H is L-swappable. Let G be a planar graph with Δ(G)≥15 and let H be the line graph of G. If L is a Δ(G)-assignment to H, then H is L-swappable. The first result is analogous to one for L-choosability by Borodin, which was later strengthened by Bonamy. The second result is analogous to another for L-choosability by Borodin, which was later strengthened by Borodin, Kostochka, and Woodall.