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arXiv · 2605.20746

Oriented Discrepancy of The Square of Hamilton Cycles

Yufei Chang·Yangyang Cheng·Zhilan Wang·Shuo Wei·Jin Yan
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Abstract

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 $\delta(G)\geq 2n/3$ contains the square of a Hamilton cycle $H$ with $\sigma_{\max}(H)$ guaranteed to exceed a function depending on $\delta(G)$ and $n$.

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Yufei Chang, Yangyang Cheng, Zhilan Wang, Shuo Wei, Jin Yan. 2026-05-20. Oriented Discrepancy of The Square of Hamilton Cycles. https://arxiv.org/abs/2605.20746

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