  The notion of robust expansion has played a central role in the solution of
several conjectures involving the packing of Hamilton cycles in graphs and
directed graphs. These and other results usually rely on the fact that every
robustly expanding (di)graph with suitably large minimum degree contains a
Hamilton cycle. Previous proofs of this require Szemer\'edi's Regularity Lemma
and so this fact can only be applied to dense, sufficiently large robust
expanders. We give a proof that does not use the Regularity Lemma and, indeed,
we can apply our result to suitable sparse robustly expanding digraphs.

Combinatorics