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The degree sequence of a graph <math>G</math> in <math>G^n</math> depends only on the number of edges in the sets

The degree sequence of a graph <math>G</math> in <math>G^n</math> depends only on the number of edges in the sets

在 <math>G^n</math> 中，图的度序列仅取决于集合中的边数。

在 <math>G^n</math> 中，图 <math>G</math> 的度序列仅取决于集合中的边数。

:<math>V_n^{(2)} = \left \{ij \ : \ 1 \leq j \leq n, i \neq j \right \} \subset V^{(2)}, \qquad  i=1, \cdots, n.</math>

:<math>V_n^{(2)} = \left \{ij \ : \ 1 \leq j \leq n, i \neq j \right \} \subset V^{(2)}, \qquad  i=1, \cdots, n.</math>

If edges, <math>M</math> in a random graph, <math>G_M</math> is large enough to ensure that almost every <math>G_M</math> has minimum degree at least 1, then almost every <math>G_M</math> is connected and, if <math>n</math> is even, almost every <math>G_M</math> has a perfect matching. In particular, the moment the last isolated vertex vanishes in almost every random graph, the graph becomes connected.

If edges, <math>M</math> in a random graph, <math>G_M</math> is large enough to ensure that almost every <math>G_M</math> has minimum degree at least 1, then almost every <math>G_M</math> is connected and, if <math>n</math> is even, almost every <math>G_M</math> has a perfect matching. In particular, the moment the last isolated vertex vanishes in almost every random graph, the graph becomes connected.

如果随机图中的边，<math>g </math > 足够大以确保几乎每个 < math > g </math > 至少有1个最小度，那么几乎每个 < math > g </math > 是连通的，如果 < math > n </math > 是偶数，几乎每个 < math > g </math > 都有一个完美的匹配。特别是，在几乎每个随机图中，最后一个孤立点消失的那一刻，图成为连通的。

如果随机图中的边 <math>M</math>，<math>G_M</math> 足够大以确保几乎每个 <math>G_M</math> 的最小阶数至少为1，那么几乎每个 <math>G</math> 是连通的，如果 <math>n</math> 是偶数，则几乎每个 <math>G_M</math> 都有一个完美的匹配。特别是，在几乎每个随机图中，最后一个孤立点消失的那一刻，图成为连通的。

Almost every graph process on an even number of vertices with the edge raising the minimum degree to 1 or a random graph with slightly more than <math>\tfrac{n}{4}\log(n)</math> edges and with probability close to 1 ensures that the graph has a complete matching, with exception of at most one vertex.

Almost every graph process on an even number of vertices with the edge raising the minimum degree to 1 or a random graph with slightly more than <math>\tfrac{n}{4}\log(n)</math> edges and with probability close to 1 ensures that the graph has a complete matching, with exception of at most one vertex.

几乎每个偶数顶点上的最小度提高到1的图或稍大于 < math > tfrac { n }{4} log (n) </math > 边且概率接近1的随机图都能确保图有完全匹配，只有最多一个顶点例外。

几乎每个偶数顶点上的最小度提高到1的图或稍大于 <math>\tfrac{n}{4}\log(n)</math> 边且概率接近1的随机图都能确保图有完全匹配，但最多只有一个顶点。