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We provide an NC algorithm for nding Hamilton cycles in directed graphs with a certain robust expansion property. This property captures several known criteria for the existence of Hamilton cycles in terms of the degree sequence and thus we provide algorithmic proofs of (i) an ‘oriented’ analogue of Dirac’s theorem and (ii) an approximate version (for directed graphs) of Chv atal’s theorem. Moreover, our main result is used as a tool

Finding Hamilton cycles in robustly expanding digraphs