随机图的秩
The Rank of Random Graphs
摘要：
我们证明了Erdös-Rényi随机图$G(n,p)$的邻接矩阵的秩几乎必然等于任意$c\ln n/n<p<1/2$的非孤立点的个数，其中$c$是大于1/2的任意正常数.特别地，巨分量（a.s.）在这个范围内都有军衔
英文摘要：
We show that almost surely the rank of the adjacency matrix of the Erdös-Rényi random graph $G(n,p)$ equals the number of non-isolated vertices for any $c\ln n/n<p<1/2$, where $c$ is an arbitrary positive constant larger than 1/2. In particular, the giant component (a.s.) has full rank in this range.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
