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Alternating paths in oriented graphs with large semidegree

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arxiv 2406.03166 v3 pith:4OROFB33 submitted 2024-06-05 math.CO

Jozef Skokan , Mykhaylo Tyomkyn This is my paper · ORCID
classification math.CO
keywords alternatingorientedsteinaddario-berrychenconjecturescontainsevery
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Antidirected paths in oriented graphs

    math.CO 2025-06 conditional novelty 7.0 of 10

    Every oriented graph with minimum pseudo-semidegree greater than (k-1+√(k-3))/2 contains an antidirected path of length k, asymptotically matching the conjectured k/2 threshold.

  2. Oriented Trees in Digraphs without Oriented $4$-cycles

    math.CO 2024-11 conditional novelty 6.0 of 10

    If a digraph has no oriented 4-cycles, minimum semidegree at least k/2, and at least one vertex with outdegree and indegree at least k, then it contains every oriented tree with k arcs.

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