Finding Partite Hypergraphs Efficiently
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918346688036864 |
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| author | Espuña, Ferran |
| author_facet | Espuña, Ferran |
| contents | We provide a deterministic polynomial-time algorithm that, for a given $k$-uniform hypergraph $H$ with $n$ vertices and edge density $d$, finds a complete $k$-partite subgraph of $H$ with parts of size at least ${c(d, k)(\log n)^{1/(k-1)}}$. This generalizes work by Mubayi and Turán on bipartite graphs. The value we obtain for the part size matches the order of magnitude guaranteed by the non-constructive proof due to Erdős and is tight up to a constant factor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_10641 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finding Partite Hypergraphs Efficiently Espuña, Ferran Combinatorics 05C65, 05C35, 90C35 We provide a deterministic polynomial-time algorithm that, for a given $k$-uniform hypergraph $H$ with $n$ vertices and edge density $d$, finds a complete $k$-partite subgraph of $H$ with parts of size at least ${c(d, k)(\log n)^{1/(k-1)}}$. This generalizes work by Mubayi and Turán on bipartite graphs. The value we obtain for the part size matches the order of magnitude guaranteed by the non-constructive proof due to Erdős and is tight up to a constant factor. |
| title | Finding Partite Hypergraphs Efficiently |
| topic | Combinatorics 05C65, 05C35, 90C35 |
| url | https://arxiv.org/abs/2508.10641 |