Geodesic
Factorially many maximum matchings close to the Erdős-Gallai bound
The electronic journal of combinatorics, Tome 29 (2022) no. 2
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A classical result of Erdős and Gallai determines the maximum size $m(n,\nu)$ of a graph $G$ of order $n$ and matching number $\nu n$. We show that $G$ has factorially many maximum matchings provided that its size is sufficiently close to $m(n,\nu)$.
DOI : 10.37236/10610
Classification : 05C70, 05C30
Mots-clés : matching number, maximum matchings 
@article{10_37236_10610,
     author = {St\'ephane Bessy and Johannes Pardey and Lucas Picasarri-Arrieta and Dieter Rautenbach},
     title = {Factorially many maximum matchings close to the {Erd\H{o}s-Gallai} bound},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {2},
     doi = {10.37236/10610},
     zbl = {1492.05125},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10610/}
}
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Stéphane Bessy; Johannes Pardey; Lucas Picasarri-Arrieta; Dieter Rautenbach. Factorially many maximum matchings close to the Erdős-Gallai bound. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10610

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