Geodesic
Perfect matching preservers
The electronic journal of combinatorics, Tome 13 (2006)
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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
Classification : 05C70, 05C20, 05C50 
@article{10_37236_1121,
     author = {Richard A. Brualdi and Martin Loebl and Ond\v{r}ej Pangr\'ac},
     title = {Perfect matching preservers},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1121},
     zbl = {1115.05069},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1121/}
}
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Richard A. Brualdi; Martin Loebl; Ondřej Pangrác. Perfect matching preservers. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1121

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