Shortest Reconfiguration of Perfect Matchings via Alternating Cycles
Data Structures and Algorithms
2019-07-04 v1 Discrete Mathematics
Abstract
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.
Keywords
Cite
@article{arxiv.1907.01700,
title = {Shortest Reconfiguration of Perfect Matchings via Alternating Cycles},
author = {Takehiro Ito and Naonori Kakimura and Naoyuki Kamiyama and Yusuke Kobayashi and Yoshio Okamoto},
journal= {arXiv preprint arXiv:1907.01700},
year = {2019}
}