Inheritance of expansion and oriented Hamilton cycles in robust expanders: a regularity-free proof

Häggkvist and Thomason proved that every $n$-vertex oriented graph with minimum semidegree at least $(\frac{5}{12}+o(1))n$ contains every orientation of a Hamilton cycle. Using Szemerédi's regularity lemma, Kelly later improved this to the asymptotically sharp bound $(\frac{3}{8}+o(1))n$. Taylor sub