An exact minimum degree condition for Hamilton cycles in oriented graphs

TL;DR

This paper proves a precise minimum degree condition for large oriented graphs to contain Hamilton cycles, solving a longstanding problem and establishing optimal bounds.

Contribution

It establishes the exact minimum degree threshold for Hamilton cycles in large oriented graphs, confirming a conjecture from 1979.

Findings

Minimum in- and outdegree at least (3n-4)/8 guarantees Hamilton cycles

The bound is proven to be best possible

Solves Thomassen's 1979 problem

Abstract

We show that every sufficiently large oriented graph with minimum in- and outdegree at least (3n-4)/8 contains a Hamilton cycle. This is best possible and solves a problem of Thomassen from 1979.