论文标题
薄缸，圆环和klein瓶网格图的2因子转移挖掘的结构
The Structure of the 2-factor Transfer Digraph common for Thin Cylinder, Torus and Klein Bottle Grid Graphs
论文作者
论文摘要
我们证明，转移digraph $ {\ cal d}^*_ {c，m} $需要在薄缸中枚举2因子$ tnc_ {m}（n）$，torus $ tg_ {m} {m} {m}（m}（n）$和klein bottle $ kb_m $ kb_m（n）$ $ $ $ $ m。顶点）当$ m $奇怪时，只有两个组件的订单$ 2^{m-1} $是同构的。当$ m $偶数时，$ {\ cal d}^*_ {c，m} $具有$ \ weft \ lfloor \ frac \ frac {m} {2} {2} \ right \ rfloor + 1 $组件，这些订单可以通过二进制数量来表达，但可以通过二进制数量和所有组合型进行表达。该证明是基于有关线性网格图（矩形，较厚的圆柱和Moebius条）的最近获得的结果的应用。
We prove that the transfer digraph ${\cal D}^*_{C,m}$ needed for the enumeration of 2-factors in the thin cylinder $TnC_{m}(n)$, torus $TG_{m}(n)$ and Klein bottle $KB_m(n)$ (all grid graphs of the fixed width $m$ and with $m \cdot n$ vertices), when $m$ is odd, has only two components of order $2^{m-1}$ which are isomorphic. When $m$ is even, ${\cal D}^*_{C,m}$ has $ \left\lfloor \frac{m}{2} \right\rfloor + 1$ components which orders can be expressed via binomial coefficients and all but one of the components are bipartite digraphs. The proof is based on the application of recently obtained results concerning the related transfer digraph for linear grid graphs (rectangular, thick cylinder and Moebius strip).
