Number of 1-factorizations of regular high-degree graphs

  title={Number of 1-factorizations of regular high-degree graphs},
  • Published 2018
A 1-factor in an n-vertex graph G is a collection n 2 vertex-disjoint edges and a 1-factorization of G is a partition of its edges into edge-disjoint 1-factors. Clearly, a 1-factorization of G cannot exist unless n is even and G is regular (that is, all vertices are of the same degree). The problem of finding 1-factorizations in graphs goes back to a paper of Kirkman in 1847 and has been extensively studied since then. Deciding whether a graph has 1-factorization is usually a very difficult… CONTINUE READING

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