报告题目:The threshold probability for long cycles
报告人：Humberto Naves, Institute for Mathematics and its Applications, USA
报告时间：8月14日15:15-16:15
摘要：For a given graph $G$ of minimum degree at least $k$, let $G_p$ denote the random spanning subgraph of $G$ obtained by retaining each edge independently with probability $p=p(k)$. In this talk, we prove that if $p /ge /frac{/log k + /log /log k + /omega_k(1)}{k}$, where $/omega_k(1)$ is any function tending to infinity with $k$, then $G_p$ asymptotically almost surely contains a cycle of length at least $k+1$. When $G$ is the complete graph on $k+1$ vertices, our theorem coincides with the classic result on the threshold probability for the existence of a Hamilton cycle in the binomial random graph.
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