Shortest perfect-matching reconfiguration via single alternating cycles is NP-hard for planar and bipartite graphs but polynomial-time solvable for outerplanar graphs.
Finding shortest paths between graph colourings.Algorithmica, 75(2):295–321, 2016
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Shortest Reconfiguration of Perfect Matchings via Alternating Cycles
Shortest perfect-matching reconfiguration via single alternating cycles is NP-hard for planar and bipartite graphs but polynomial-time solvable for outerplanar graphs.