Hamilton Cycles in Dense Regular Digraphs and Oriented Graphs
Abstract
We prove that for every > 0 there exists n0=n0() such that every regular oriented graph on n > n0 vertices and degree at least (1/4 + )n has a Hamilton cycle. This establishes an approximate version of a conjecture of Jackson from 1981. We also establish a result related to a conjecture of K\"uhn and Osthus about the Hamiltonicity of regular directed graphs with suitable degree and connectivity conditions.
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