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arXiv · 2505.05606

Perfect tilings of 3-graphs with the generalised triangle

Candida Bowtell·Amarja Kathapurkar·Natasha Morrison·Richard Mycroft
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Abstract

We establish a best-possible minimum codegree condition for the existence of a perfect tiling of a $3$-uniform hypergraph $H$ with copies of the generalised triangle $T$, which is the 3-uniform hypergraph with five vertices $a, b, c, d, e$ and three edges $abc$, $abd$, $cde$. We also give an asymptotically-optimal minimum codegree condition for the rainbow version of the problem.

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Candida Bowtell, Amarja Kathapurkar, Natasha Morrison, Richard Mycroft. 2025-05-08. Perfect tilings of 3-graphs with the generalised triangle. https://arxiv.org/abs/2505.05606

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