Abstract

The calculation of the set of all simple paths connecting two vertices of an undirected graph is considered. The more general problems of connecting vertices which belong to disjoint sets of vertices in a graph by all simple paths are also investigated. The connection between these problems and finding vertex biconnected components and graph bridges is established, and based on this their complete solutions are given. Simplifying techniques for the calculation of the sets of paths based on the addition of auxiliary edges and vertices to the analyzed graph are proposed. Examples of the application of the developed apparatus to problems of the real-time management of transport networks are given.

中文翻译：

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运输网络中简单路径图的构造：I.一般解决方案和示例

摘要

考虑了连接无向图的两个顶点的所有简单路径的集合的计算。还研究了通过所有简单路径连接属于图形中不相交的顶点集的顶点的更一般的问题。建立了这些问题之间的联系，并找到了顶点双向连接的组件和图桥，并在此基础上给出了其完整的解决方案。提出了一种简化的技术，用于在将辅助边和顶点添加到所分析的图形的基础上来计算路径集。给出了将所开发的装置应用于运输网络的实时管理问题的例子。