2025/01/10 by Ai, Jiangdong, Qiwen Guo, Guo, Qiwen +10
Computer Science · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.2501.05968
openalex publication_date 2025/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Erd\H os (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 ≥ 3 vertices with minimum degree δ(D) ≥ 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.