What question did this study set out to answer?

The aim is to generalize Ghouila-Houri's theorem on directed Hamilton cycles to transversal digraphs.

Transversal Hamilton cycles in digraph collections

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The aim is to generalize Ghouila-Houri's theorem on directed Hamilton cycles to transversal digraphs.
Defined transversal digraphs in relation to collections of digraphs.
Applied the absorption method for transversals.
Utilized the regularity method for digraph collections.
Employed the transversal blow-up lemma in proof.
Established a transversal version of Hamilton's cycle theorem in digraphs.
Showed that large digraphs with minimum semi-degree contain a transversal Hamilton cycle.
Proved connection to Dirac’s theorem under certain conditions.

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Demonstrates the transversal Hamilton cycle in digraph collections, implying new results in graph theory.

Cheng et al. (2026) studied this question.

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