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}. Seb\"o 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-Lov\'asz canonical decomposition.
翻译:本文是一系列论文的首页, 这些论文提供了对双面图中最大外观包装的定性。 在一张链接的图表中, 一组偶数的顶点和最小的外观的外观, 可以定义边缘加权, 从而可以界定脊椎之间的距离 。 此外, 根据一个指定的顶点叫做 root, 顶点可以按照与根的距离进行分类, 这种顶点分类可以用来定义称为 hiem 距离 元件的子集。 Seb\ “ o” 提供了显示距离元件、 最小值的T$- joins 和 $T$- cutes之间的关系的理论。 在本文中, 我们进一步调查两面图中的距离元组成部分的结构 。 特别是, 我们关注 em apital} 距离元, 包括根的部件 。 我们用 Kotzig- Lov\ “ asz” common depossicial position superficial ficial ficial ficial ficial plation fitudefitult。