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author:

Chen, Bin (Chen, Bin.) [1] | Hou, Xinmin (Hou, Xinmin.) [2] | Zhou, Xinyu (Zhou, Xinyu.) [3]

Indexed by:

Scopus SCIE

Abstract:

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.

Keyword:

Anticycle Antipath Minimum pseudo-semi-degree Oriented graph

Community:

  • [ 1 ] [Chen, Bin]Fuzhou Univ, Sch Math & Stat, Fuzhou 350108, Peoples R China
  • [ 2 ] [Chen, Bin]Hefei Natl Lab, Hefei 230088, Peoples R China
  • [ 3 ] [Hou, Xinmin]Hefei Natl Lab, Hefei 230088, Peoples R China
  • [ 4 ] [Hou, Xinmin]Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
  • [ 5 ] [Zhou, Xinyu]Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
  • [ 6 ] [Hou, Xinmin]Univ Sci & Technol China, Key Lab Wu Wen Tsun Math, CAS, Hefei 230026, Anhui, Peoples R China

Reprint 's Address:

  • [Hou, Xinmin]Hefei Natl Lab, Hefei 230088, Peoples R China;;[Hou, Xinmin]Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China;;[Hou, Xinmin]Univ Sci & Technol China, Key Lab Wu Wen Tsun Math, CAS, Hefei 230026, Anhui, Peoples R China

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Source :

DISCRETE MATHEMATICS

ISSN: 0012-365X

Year: 2025

Issue: 5

Volume: 348

0 . 7 0 0

JCR@2023

CAS Journal Grade:4

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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