Oriented Discrepancy of The Square of Hamilton Cycles
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914581991915520 |
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| author | Chang, Yufei Cheng, Yangyang Wang, Zhilan Wei, Shuo Yan, Jin |
| author_facet | Chang, Yufei Cheng, Yangyang Wang, Zhilan Wei, Shuo Yan, Jin |
| contents | For an oriented graph $G$, the oriented discrepancy problem concerns the existence of a spanning subgraph of $G$ with a large imbalance between its forward and backward edge orientations. Freschi and Lo proved the Dirac-type Hamilton cycle result in oriented graphs, and asked for an analogue for powers of Hamilton cycles under a minimum-degree condition. We show that, for sufficiently large $n$, every oriented graph $G$ on $n$ vertices with minimum degree $δ(G)\geq 2n/3$ contains the square of a Hamilton cycle $H$ with $σ_{\max}(H)$ guaranteed to exceed a function depending on $δ(G)$ and $n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_20746 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Oriented Discrepancy of The Square of Hamilton Cycles Chang, Yufei Cheng, Yangyang Wang, Zhilan Wei, Shuo Yan, Jin Combinatorics 05C07, 05C20, 05C35 For an oriented graph $G$, the oriented discrepancy problem concerns the existence of a spanning subgraph of $G$ with a large imbalance between its forward and backward edge orientations. Freschi and Lo proved the Dirac-type Hamilton cycle result in oriented graphs, and asked for an analogue for powers of Hamilton cycles under a minimum-degree condition. We show that, for sufficiently large $n$, every oriented graph $G$ on $n$ vertices with minimum degree $δ(G)\geq 2n/3$ contains the square of a Hamilton cycle $H$ with $σ_{\max}(H)$ guaranteed to exceed a function depending on $δ(G)$ and $n$. |
| title | Oriented Discrepancy of The Square of Hamilton Cycles |
| topic | Combinatorics 05C07, 05C20, 05C35 |
| url | https://arxiv.org/abs/2605.20746 |