Jaehoon Kim (김재훈), A resilience version of Pósa’s theorem

Pósa’s theorem states that any graph G whose degree sequence $d_1\le \cdots \le d_n$ satisfies $d_i\ge i+1$ for all $i<n/2$ has a Hamilton cycle. This degree condition is best possible. We show that a similar result holds for suitable subgraphs $G$ of random graphs. This is joint work with Padraig Condon, Alberto Espuny Diaz, Daniela Kühn and Deryk Osthus.