Perfect tilings of 3-graphs with the generalised triangle
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913828017537024 |
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| author | Bowtell, Candida Kathapurkar, Amarja Morrison, Natasha Mycroft, Richard |
| author_facet | Bowtell, Candida Kathapurkar, Amarja Morrison, Natasha Mycroft, Richard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perfect tilings of 3-graphs with the generalised triangle Bowtell, Candida Kathapurkar, Amarja Morrison, Natasha Mycroft, Richard Combinatorics 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. |
| title | Perfect tilings of 3-graphs with the generalised triangle |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.05606 |