Title

Connected Cubic Graphs with the Maximum Number of Perfect Matchings

Publication Date

6-24-2020

Document Type

Article

Abstract

It is proved that for $n \geq 6$, the number of perfect matchings in a simple connected cubic graph on $2n$ vertices is at most $4 f_{n-1}$, with $f_n$ being the $n$-th Fibonacci number. The unique extremal graph is characterized as well. In addition, it is shown that the number of perfect matchings in any cubic graph $G$ equals the expected value of a random variable defined on all $2$-colorings of edges of $G$. Finally, an improved lower bound on the maximum number of cycles in a cubic graph is provided.

Publication Title

arXiv:2006.13459 [math]

Publisher Policy

No SHERPA/RoMEO policy available

Open Access Status

OA Disciplinary Repository

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