论文标题
Möbius梯子和棱镜中的完美比赛数量
The Number of Perfect Matchings in Möbius Ladders and Prisms
论文作者
论文摘要
1970年代的Lovász和Plummer的猜想认为，任何$ 3 $等级的图表中的完美匹配数在2011年被Esperet，Kardoš，King，Král'和Norine证明。我们提供了两个$ 3 $等级图的家族中完美匹配数量的确切公式。在图表中，由$ 2n $ cycle带有直径和弦（也称为Möbius梯子$ m_n $和harary图），以及在周期$ c_n $的笛卡尔产品中，带有边缘（称为周期Prism）（称为周期prism），匹配的数量是fibonacci Number of fibonacci nubmes $ f_ f_ f_ f _ n-1 $ f_ {当$ n $是奇怪的阶梯时，对于$ n $均匀的循环棱镜。
The 1970s conjecture of Lovász and Plummer that the number of perfect matchings in any $3$-regular graph is exponential in the number of vertices was proved in 2011 by Esperet, Kardoš, King, Král', and Norine. We give the exact formula for the number of perfect matchings in two families of $3$-regular graphs. In the graph consisting of a $2n$-cycle with diametric chords (also known as the Möbius ladder $M_n$ and a Harary graph) and in the cartesian product of the cycle $C_n$ with an edge (called the cycle prism), the number of matchings is the sum of the Fibonacci numbers $F_{n-1}$ and $F_{n+1}$, plus two more for the Möbius ladder when $n$ is odd and for the cycle prism when $n$ is even.
