论文标题
在完整时间图中由汉密尔顿时间路径产生的矢量空间的基础
Basis for a vector space generated by Hamiltonian time paths in a complete time graph
论文作者
论文摘要
在本文中，我们介绍了顺序n的完整时间图的概念。我们在完整的时间图中定义时间路径和哈密顿时间路径。每个汉密尔顿的时路（HTP）与整数1至n的一些排列P相关。该路径的特征函数在竞争时间图的边缘集合的矢量空间中形成矢量。我们将考虑这些功能产生的向量空间。本文的主要结果是确定该向量空间的n尺寸大于或等于5。我们还提供了一种算法，其复杂性以在该矢量空间中建立基础。
In this paper we introduce the notion of a complete time graph of order n. We define time paths and Hamiltonian time paths in a complete time graph. Each Hamiltonian time path (htp) is associated with some permutation p of the integers 1 to n. The characteristic function of this path forms a vector in the vector space of rational-valued functions on the set of edges of the compete time graph. We will consider the vector space generated by these functions. The main result in this paper is to determine the dimension of this vector space for n greater than or equal to 5. We also give an algorithm with its complexity for the construction of a basis in this vector space.
