Shortest perfect-matching reconfiguration via single alternating cycles is NP-hard for planar and bipartite graphs but polynomial-time solvable for outerplanar graphs.
Complexity of token swapping and its variants.Algorithmica, 80(9):2656–2682, 2018
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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.