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arXiv · 2602.13737

Cycle tilings and $H$-factors in directed graphs

Theodore Molla·Andrew Treglown
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Abstract

We prove several results concerning cycle tilings and $H$-factors in digraphs. We provide a minimum semi-degree condition for forcing a digraph to contain a given spanning collection of vertex-disjoint orientations of cycles. Our result is asymptotically best possible for odd cycles and can be viewed as a digraph analogue of the El-Zahar conjecture. In addition, we asymptotically determine the minimum degree threshold for forcing an $H$-factor in a digraph for a range of digraphs $H$, including the cases when $H$ is a tree or anti-directed cycle. Furthermore, an asymptotically exact Ore-type result for forcing a transitive tournament factor in a digraph is proven. Several related open problems are also highlighted.

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Theodore Molla, Andrew Treglown. 2026-02-14. Cycle tilings and $H$-factors in directed graphs. https://arxiv.org/abs/2602.13737

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