Corpus ID: 119135299

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}
}
  • Gasper Fijavz, Matthias Kriesell
  • Published 2016
  • Mathematics
  • arXiv: Combinatorics
  • 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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