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Let delta(D) be the minimum semi-degree of an oriented graph D. Jackson (1981) proved that every oriented graph D with delta(D) >= k contains a directed path of length 2k when | V (D)| > 2k + 2, and a directed Hamilton cycle when | V (D)| <= 2k + 2. Stein (2020) further conjectured that every oriented graph D with delta(D) > k/2 contains any orientated path of length k. Recently, Klimosov & aacute; and Stein (2023) introduced the minimum pseudo-semidegree delta(D) (A slightly weaker variant of the minimum semi-degree condition as delta(D) >= delta(D)) and showed that every oriented graph D with delta(D) >= (3k - 2)/4 contains each antipath of length k for k >= 3. In this paper, we improve the result of Klimosov & aacute; and Stein by showing that for all k >= 2, every oriented graph with delta(D) >= (2k + 1)/3 contains either an antipath of length at least k + 1 or an anticycle of length at least k + 1. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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DISCRETE MATHEMATICS
ISSN: 0012-365X
Year: 2025
Issue: 5
Volume: 348
0 . 7 0 0
JCR@2023
CAS Journal Grade:4
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ESI Highly Cited Papers on the List: 0 Unfold All
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30 Days PV: 1
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