论文标题
连接的立方图，最大数量完美匹配
Connected cubic graphs with the maximum number of perfect matchings
论文作者
论文摘要
事实证明，对于$ n \ geq 6 $，在$ 2N $ vertices上的简单连接的立方图中的完美匹配数最多是$ 4 f_ {n-1} $，其中$ f_n $是$ n $ th fibonacci编号。独特的极端图也被描述了。此外，可以证明，任何立方图$ g $中的完美匹配数量等于在所有$ 2 $ os of $ g $的$ 2 $颜色上定义的随机变量的预期值。最后，提供了立方图中最大循环数的改进下限。
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.
