Arbitrary orientations of Hamilton cycles in digraphs

Louis DeBiasio, Daniela Kühn, Theodore Molla, Deryk Osthus, Amelia Taylor

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
124 Downloads (Pure)


Let n be sufficiently large and suppose that G is a digraph on n vertices where every vertex has in- and outdegree at least n/2. We show that G contains every orientation of a Hamilton cycle except, possibly, the antidirected one. The antidirected case was settled by DeBiasio and Molla, where the threshold is n/2 + 1. Our result is best possible and improves on an approximate result by HÂaggkvist and Thomason.

Original languageEnglish
Pages (from-to)1553-1584
Number of pages32
JournalSIAM Journal on Discrete Mathematics
Issue number3
Publication statusPublished - 2015


  • Digraphs
  • Extremal problems
  • Hamilton cycles
  • Robust expanders

ASJC Scopus subject areas

  • Mathematics(all)


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