论文标题
在完整图上的Conway-Gordon定理和固有链接的概括
Generalization of the Conway-Gordon theorem and intrinsic linking on complete graphs
论文作者
论文摘要
康威（Conway）和戈登（Gordon）证明，对于六个顶点上的每个空间完整图，所有组成型两个组成链接的链接数量的总和是奇怪的，而Kazakov和Korablev证明，对于每个空间完整图，具有任意数量的顶点的每个空间完整图，大于六个大于六个的链接数量，所有组成型链接的链接总和是所有链接的链接的总和。在本文中，我们表明，对于每个空间完整图，其顶点的数量大于六，链接数的平方之和在所有两个组件的汉密尔顿链路上都是根据所有三角形三角形构成链接的总和明确确定的。作为一个应用程序，我们表明，如果顶点的数量足够大，那么每个空间完整图都包含一个两个组件的汉密尔顿链接，其链接数的绝对值是任意较大的。还给出了一些直线空间完整图的应用。
Conway and Gordon proved that for every spatial complete graph on six vertices, the sum of the linking numbers over all of the constituent two-component links is odd, and Kazakov and Korablev proved that for every spatial complete graph with arbitrary number of vertices greater than six, the sum of the linking numbers over all of the constituent two-component Hamiltonian links is even. In this paper, we show that for every spatial complete graph whose number of vertices is greater than six, the sum of the square of the linking numbers over all of the two-component Hamiltonian links is determined explicitly in terms of the sum over all of the triangle-triangle constituent links. As an application, we show that if the number of vertices is sufficiently large then every spatial complete graph contains a two-component Hamiltonian link whose absolute value of the linking number is arbitrary large. Some applications to rectilinear spatial complete graphs are also given.
