Kempe equivalent list colorings revisited

Abstract

AbstractA Kempe chain on colors and is a component of the subgraph induced by colors and . A Kempe change is the operation of interchanging the colors of some Kempe chains. For a list‐assignment and an ‐coloring , a Kempe change is ‐valid for if performing the Kempe change yields another ‐coloring. Two ‐colorings are ‐equivalent if we can form one from the other by a sequence of ‐valid Kempe changes. A degree‐assignment is a list‐assignment such that for every . Cranston and Mahmoud asked: For which graphs and degree‐assignment of is it true that all the ‐colorings of are ‐equivalent? We prove that for every 4‐connected graph which is not complete and every degree‐assignment of , all ‐colorings of are ‐equivalent.