arXiv Open Access 2025

Oriented discrepancy of Hamilton cycles in oriented graphs satisfying Ore-type condition

Jiangdong Ai Qiwen Guo Gregory Gutin Yongxin Lan Qi Shao +2 lainnya
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Abstrak

Erd{\H o}s (1963) initiated extensive graph discrepancy research on 2-edge-colored graphs. Gishboliner, Krivelevich, and Michaeli (2023) launched similar research on oriented graphs. They conjectured the following extension of Dirac's theorem: If $D$ is an oriented graph on $n \ge 3$ vertices with minimum degree $δ(D) \ge n/ 2$, then $D$ contains a Hamilton oriented cycle with at least $δ(D)$ arcs in the same direction. This conjecture was proved by Freschi and Lo (2024) who posed an open problem to extend their result to an Ore-type condition. We propose two conjectures for such extensions and prove results which provide support to the conjectures.

Topik & Kata Kunci

Penulis (7)

J

Jiangdong Ai

Q

Qiwen Guo

G

Gregory Gutin

Y

Yongxin Lan

Q

Qi Shao

A

Anders Yeo

Y

Yacong Zhou

Format Sitasi

Ai, J., Guo, Q., Gutin, G., Lan, Y., Shao, Q., Yeo, A. et al. (2025). Oriented discrepancy of Hamilton cycles in oriented graphs satisfying Ore-type condition. https://arxiv.org/abs/2501.05968

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