论文标题
两分性抗激素
Antifactors in bipartite multigraphs
论文作者
论文摘要
令$ g $是带有两部分$（u，v）$的$ q $ regratular二手图。 Lu，Wang和Yan在2020年证明了$ g $具有一个跨度的子图$ h $，因此$ u $ $ u $的每个顶点在$ h $中具有1级，$ h $中的每个顶点$ v $都与$ h $中的1个不同。我们将结果扩展到了多编码，条件是$ Q $是主要的力量，并且$ g $的完美匹配数量不可除以$ Q $。多编码需要完美匹配的条件。 我们以一个猜想的猜想，内容涉及完美匹配数的限制分布模式$ q $在随机的两部分$ q $ -Regrumar图中。
Let $G$ be a $q$-regular bipartite graph with bipartition $(U,V)$. It was proved by Lu, Wang, and Yan in 2020 that $G$ has a spanning subgraph $H$ such that each vertex of $U$ has degree 1 in $H$, and each vertex of $V$ has degree distinct from 1 in $H$. We extend the result to multigraphs, under the condition that $q$ is a prime power and the number of perfect matchings of $G$ is not divisible by $q$. The condition on the number of perfect matchings is necessary for multigraphs. We conclude with a conjecture on the limiting distribution of the number of perfect matchings modulo $q$ in a random bipartite $q$-regular graph.
