Long antipaths in oriented graphs

Yuping Gao; Allan Lo

Long antipaths in oriented graphs

Combinatorics 2026-07-27 v1

Authors: Yuping Gao , Allan Lo

Abstract

An antidirected path is an oriented path in which every vertex sees either just incoming or just outgoing edges. We prove that every oriented graph with minimum semidegree at least $k$ contains an antidirected path of length $2 k -1$ . This confirms a conjecture of Stein.

Cite

@article{arxiv.2607.24738,
  title  = {Long antipaths in oriented graphs},
  author = {Yuping Gao and Allan Lo},
  journal= {arXiv preprint arXiv:2607.24738},
  year   = {2026}
}

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15 pages