Alternating paths in oriented graphs with large semidegree
Combinatorics
2025-09-08 v3
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.
Keywords
Cite
@article{arxiv.2406.03166,
title = {Alternating paths in oriented graphs with large semidegree},
author = {Jozef Skokan and Mykhaylo Tyomkyn},
journal= {arXiv preprint arXiv:2406.03166},
year = {2025}
}
Comments
minor changes, bibliography updated, 7 pages, final version