Perfect Matching Preservers

Richard A. Brualdi, Martin Loebl, Ondřej Pangrác
2006 Electronic Journal of Combinatorics  
For two bipartite graphs $G$ and $G'$, a bijection $\psi: E(G) \rightarrow E(G')$ is called a (perfect) matching preserver provided that $M$ is a perfect matching in $G$ if and only if $\psi(M)$ is a perfect matching in $G'$. We characterize bipartite graphs $G$ and $G'$ which are related by a matching preserver and the matching preservers between them.
doi:10.37236/1121 fatcat:ss7ifqzvlvclvor72hfo7zrgrm