Arbitrary Orientations of Hamilton Cycles in Oriented Graphs

Luke Kelly


We use a randomised embedding method to prove that for all $\alpha>0$ any sufficiently large oriented graph $G$ with minimum in-degree and out-degree $\delta^+(G),\delta^-(G)\geq (3/8+\alpha)|G|$ contains every possible orientation of a Hamilton cycle. This confirms a conjecture of Häggkvist and Thomason.

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