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Shortest Reconfiguration of Perfect Matchings via Alternating Cycles

Ito, Takehiro Kakimura, Naonori Kamiyama, Naoyuki Kobayashi, Yusuke Okamoto, Yoshio 京都大学 DOI:10.1137/20m1364370

2022

概要

Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of perfect matchings via alternating cycles. Namely, we want to find a shortest sequence of perfect matchings which transforms one given perfect matching to another given perfect matching such that the symmetric difference of each pair of consecutive perfect matchings is a single cycle. The problem is equivalent to the combinatorial shortest path problem in perfect matching polytopes. We prove that the problem is NP-hard even when a given graph is planar or bipartite, but it can be solved in polynomial time when the graph is outerplanar.

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