二部移植中的紧割Ⅰ：资本距离分量
Tight Cuts in Bipartite Grafts I: Capital Distance Components
摘要：
本文是第一个从一系列的文件，提供了一个表征的最大包装的$T$ -削减二部图。给定一个连通图，一个偶数顶点的集合$T$，和一个最小$T$ -连接，可以定义一个边权重，从中可以定义顶点之间的距离。此外，给定一个称为根的指定顶点，顶点可以根据它们到根的距离进行分类，并且顶点的这种分类可以用于定义称为{ \em距离分量}的子图族。Sebö提供了一个定理，揭示了距离分量、最小$T$ -连接和$T$ -切割之间的关系。本文进一步研究了二部图中距离分量的结构。特别地，我们关注{ \em capital}距离分量，即包括根的距离分量。我们揭示了资本的距离组件的结构方面的$T$ -加入模拟的一般Kotzig-Lovász典型分解。
英文摘要：
This paper is the first from a series of papers that provide a characterization of maximum packings of $T$-cuts in bipartite graphs. Given a connected graph, a set $T$ of an even number of vertices, and a minimum $T$-join, an edge weighting can be defined, from which distances between vertices can be defined. Furthermore, given a specified vertex called root, vertices can be classified according to their distances from the root, and this classification of vertices can be used to define a family of subgraphs called {\em distance components}. Sebö provided a theorem that revealed a relationship between distance components, minimum $T$-joins, and $T$-cuts. In this paper, we further investigate the structure of distance components in bipartite graphs. Particularly, we focus on {\em capital} distance components, that is, those that include the root. We reveal the structure of capital distance components in terms of the $T$-join analogue of the general Kotzig-Lovász canonical decomposition.
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