Hypergraph removal with polynomial bounds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866918044531425280 |
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| author | Gishboliner, Lior Shapira, Asaf |
| author_facet | Gishboliner, Lior Shapira, Asaf |
| contents | Given a fixed $k$-uniform hypergraph $F$, the $F$-removal lemma states that every hypergraph with few copies of $F$ can be made $F$-free by the removal of few edges. Unfortunately, for general $F$, the constants involved are given by incredibly fast-growing Ackermann-type functions. It is thus natural to ask for which $F$ one can prove removal lemmas with polynomial bounds. One trivial case where such bounds can be obtained is when $F$ is $k$-partite. Alon proved that when $k=2$ (i.e. when dealing with graphs), only bipartite graphs have a polynomial removal lemma. Kohayakawa, Nagle and Rödl conjectured in 2002 that Alon's result can be extended to all $k>2$, namely, that the only $k$-graphs $F$ for which the hypergraph removal lemma has polynomial bounds are the trivial cases when $F$ is $k$-partite. In this paper we prove this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_07567 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hypergraph removal with polynomial bounds Gishboliner, Lior Shapira, Asaf Combinatorics Given a fixed $k$-uniform hypergraph $F$, the $F$-removal lemma states that every hypergraph with few copies of $F$ can be made $F$-free by the removal of few edges. Unfortunately, for general $F$, the constants involved are given by incredibly fast-growing Ackermann-type functions. It is thus natural to ask for which $F$ one can prove removal lemmas with polynomial bounds. One trivial case where such bounds can be obtained is when $F$ is $k$-partite. Alon proved that when $k=2$ (i.e. when dealing with graphs), only bipartite graphs have a polynomial removal lemma. Kohayakawa, Nagle and Rödl conjectured in 2002 that Alon's result can be extended to all $k>2$, namely, that the only $k$-graphs $F$ for which the hypergraph removal lemma has polynomial bounds are the trivial cases when $F$ is $k$-partite. In this paper we prove this conjecture. |
| title | Hypergraph removal with polynomial bounds |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2202.07567 |