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
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.
Penulis (7)
J
Jiangdong Ai
Q
Qiwen Guo
G
Gregory Gutin
Y
Yongxin Lan
Q
Qi Shao
A
Anders Yeo
Y
Yacong Zhou
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