# On minimal graphs containing k perfect matchings

@article{Fijavz2016OnMG, title={On minimal graphs containing k perfect matchings}, author={Gasper Fijavz and Matthias Kriesell}, journal={arXiv: Combinatorics}, year={2016} }

We call a finite undirected graph minimally k-matchable if it has at least k distinct perfect matchings but deleting any edge results in a graph which has not. An odd subdivision of some graph G is any graph obtained by replacing every edge of G by a path of odd length connecting its end vertices such that all these paths are internally disjoint. We prove that for every k>0 there exists a finite set of graphs S(k) such that every minimally k-matchable graph is isomorphic to a disjoint union of… CONTINUE READING

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