Oriented discrepancy of Hamilton cycles in oriented graphs satisfying Ore-type condition
Abstract
Erdős (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 $ \delta (D) \ge n/ 2 $, then $ D $ contains a Hamilton oriented cycle with at least $ \delta(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 proposed two conjectures for such extensions and proved results which provided support to the conjectures.
Fields of Study & Subjects
Mathematical Approximation and Integration
Graph theory and applications
Coding theory and cryptography
Publication details
- Journal / source
- AIMS Mathematics
- Volume
- 11
- Issue
- 8
- Pages
- 24106–24119
- Publication date
- 1 January 2026
- Language
- EN