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arXiv · 2406.03166

Alternating paths in oriented graphs with large semidegree

Jozef Skokan·Mykhaylo Tyomkyn
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Abstract

In new progress on conjectures of Stein, and Addario-Berry, Havet, Linhares Sales, Reed and Thomassé, 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 Klimošová and Stein, and Chen, Hou and Zhou.

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Jozef Skokan, Mykhaylo Tyomkyn. 2025-09-05. Alternating paths in oriented graphs with large semidegree. https://arxiv.org/abs/2406.03166

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