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 H\"aggkvist and Thomason.Comment: Final version, to appear in SIAM Journal Discrete Mathematics (SIDMA

DeBiasio, Louis

Kühn, Daniela

Molla, Theodore

Osthus, Deryk

Taylor, Amelia

English

arXiv

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.</p

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Arbitrary orientations of Hamilton cycles in digraphs

Abstract. 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 Häggkvist and Thomason. 1

Arbitrary Orientations of Hamilton Cycles in Digraphs

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