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October 16, 2025Open Access

Arbitrary orientations of Hamilton cycles in directed graphs of large minimum degree

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Every directed graph with minimum degree at least (1+o(1))n contains every orientation of a Hamilton cycle, except when not strongly connected.
Ghouila-Houri's 1960 result established a Hamilton cycle in strongly connected directed graphs with minimum degree at least n.
This generalization implies that the given minimum degree condition facilitates orientations of cycles of various lengths in directed graphs.
Orientation conditions extend beyond Hamilton cycles to include a variety of directed cycles in the corresponding graphs.

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Implication

Asymptotic findings reveal that directed graphs with high minimum degree include Hamilton cycle orientations, suggesting broader implications for graph theory.

Cite This Study

DeBiasio et al. (2025) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd1b0 https://doi.org/10.48550/arxiv.2505.09793

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Implication

Asymptotic findings reveal that directed graphs with high minimum degree include Hamilton cycle orientations, suggesting broader implications for graph theory.

Arbitrary orientations of Hamilton cycles in directed graphs of large minimum degree

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Discussion

Implication

Cite This Study

Arbitrary orientations of Hamilton cycles in directed graphs of large minimum degree

Key Points

Discussion

Implication

Cite This Study

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