标题： 构造性特征对于双向图的关键图的类比 I：径向和半径的主要类别的描述 显示英文标题

标题： Constructive Characterization for Bidirected Analogue of Critical Graphs I: Principal Classes of Radials and Semiradials

摘要： 本文是系列论文的第一篇，这些论文为称为radials和semiradials的双向图类提供构造性表征。 在本文中，我们为五种主要的radials和semiradials类提供构造性表征，以便用于表征一般的radials和semiradials。 一个双向图是一个图，其中每条边的每个端点都有一个符号$+$或$-$。 双向图是有向图和带符号图的常见推广。 我们定义了一个新的radials概念，作为匹配理论中经典概念——临界图的推广。 radials也是已知称为流图的有向图类的推广。 我们还定义了semiradials，它们是radials的一个放松概念。 我们进一步定义了radials和semiradials的特殊类，即绝对semiradials、强和几乎强的radials、线性semiradials和次线性radials。 我们为这五类双向图提供了构造性表征。 我们的系列论文是建立双向图强分量分解的一系列工作的一部分。 显示英文摘要

摘要： This paper is the first from serial papers that provide constructive characterizations for classes of bidirected graphs known as radials and semiradials. In this paper, we provide constructive characterizations for five principle classes of radials and semiradials to be used for characterizing general radials and semiradials. A bidirected graph is a graph in which each end of each edge has a sign $+$ or $-$. Bidirected graphs are a common generalization of digraphs and signed graphs. We define a new concept of radials as a generalization of a classical concept in matching theory, critical graphs. Radials are also a generalization of a class of digraphs known as flowgraphs. We also define semiradials, which are a relaxed concept of radials. We further define special classes of radials and semiradials, that is, absolute semiradials, strong and almost strong radials, linear semiradials, and sublinear radials. We provide constructive characterizations for these five classes of bidirected graphs. Our serial papers are a part of a series of works that establish the strong component decomposition for bidirected graphs.