Cheng-Li Li

A near-linear Chv\'atal--Erd\H{o}s condition for Hamilton cycles in digraphs

For a digraph $D$, let $\alpha_2(D)$ be the largest size of a vertex set containing no directed $2$-cycle. Let $f_2(a)$ be the least positive integer $k$ such that every $k$-strongly connected digraph $D$ with $\alpha_2(D)\le a$ has a Hamilton cycle. Jackson and Ordaz conjectured that $f_2(a)\le a+1$. Towards this conj...