Alternating paths in oriented graphs with large semidegree
Jozef Skokan, Mykhaylo Tyomkyn
Published: 2024/6/5
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.