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SUMMARYWe study the problem of reconfiguring one list edgecoloring of a graph into another list edge-coloring by changing only one edge color assignment at a time, while at all times maintaining a list edgecoloring, given a list of allowed colors for each edge. Ito, Kamiński and Demaine gave a sufficient condition so that any list edge-coloring of a tree can be transformed into any other. In this paper, we give a new sufficient condition which improves the known one. Our sufficient condition is best possible in some sense. The proof is constructive, and yields a polynomial-time algorithm that finds a transformation between two given list edge-colorings of a tree with n vertices via O(n 2 ) recoloring steps. We remark that the upper bound O(n 2 ) on the number of recoloring steps is tight, because there is an infinite family of instances on paths that satisfy our sufficient condition and whose reconfiguration requires Ω(n 2 ) recoloring steps.

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