中文摘要：

一个图G是匹配覆盖的（或1-可扩的）如果它是连通的且G的每条边都被包含在一个完美匹配里。我们称一个图G为双因子临界的，如果对于G中的任意两个不同顶点x, y，G-x-y都有一个完美匹配。一个双因子临界图被称为砖块，如果它是3-连通的。本文对于双因子临界图与匹配覆盖二部图确定了它们的阈函数。对于非二部的匹配覆盖图，我们发现了一个概率序列，其表现就像一个阈。此外，我们证明几乎所有的3-连通图均是砖块。

英文摘要：

A graph G is matching-covered （or 1-extendable） if it is connected and every edge of G is contained in a perfect matching. We call a graph G bicritical if G-x-y has a perfect matching for every pair of distinct vertices x and y in G. A bicritical graph is called a brick if it is 3-connected. In this paper, we determine thresholds for bicritical graphs and matching-covered bipartite graphs. For non-bipartite matching-covered graphs, we find a probability sequence which acts the same way like a threshold. Furthermore, we show that asymptotically almost surely all 3-connected graphs are bricks.