Alternating paths in oriented graphs with large semidegree

TL;DR

This paper proves that oriented graphs with sufficiently large in- and out-degrees always contain long alternating paths, advancing conjectures by Stein and others.

Contribution

It establishes a new bound for the existence of long alternating paths in oriented graphs with large semidegree, improving previous results.

Findings

Graphs with all degrees > 5k/8 contain an alternating path of length k

Improves bounds on degree conditions for long paths in oriented graphs

Advances conjectures by Stein and others

Abstract

In new progress on conjectures of Stein, and Addario-Berry, Havet, Linhares Sales, Reed and Thomass\'e, we prove that every oriented graph with all in- and out-degrees greater than 5k/8 contains an alternating path of length k. This improves on previous results of Klimo\v{s}ov\'a and Stein, and Chen, Hou and Zhou.