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
Recommended Citation
Horak, P., & Kim, D. (2020). Connected Cubic Graphs with the Maximum Number of Perfect Matchings. ArXiv:2006.13459 [Math]. http://arxiv.org/abs/2006.13459
