Extremal Numbers of Hypergraph Suspensions of Even Cycles
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916131563896832 |
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| author | Mukherjee, Sayan |
| author_facet | Mukherjee, Sayan |
| contents | For fixed $k\ge 2$, determining the order of magnitude of the number of edges in an $n$-vertex bipartite graph not containing $C_{2k}$, the cycle of length $2k$, is a long-standing open problem. We consider an extension of this problem to triple systems. In particular, we prove that the maximum number of triples in an $n$-vertex triple system which does not contain a $C_6$ in the link of any vertex, has order of magnitude $n^{7/3}$. Additionally, we construct new families of dense $C_6$-free bipartite graphs with $n$ vertices and $n^{4/3}$ edges in order of magnitude. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_06743 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Extremal Numbers of Hypergraph Suspensions of Even Cycles Mukherjee, Sayan Combinatorics 05C65, 05C38 For fixed $k\ge 2$, determining the order of magnitude of the number of edges in an $n$-vertex bipartite graph not containing $C_{2k}$, the cycle of length $2k$, is a long-standing open problem. We consider an extension of this problem to triple systems. In particular, we prove that the maximum number of triples in an $n$-vertex triple system which does not contain a $C_6$ in the link of any vertex, has order of magnitude $n^{7/3}$. Additionally, we construct new families of dense $C_6$-free bipartite graphs with $n$ vertices and $n^{4/3}$ edges in order of magnitude. |
| title | Extremal Numbers of Hypergraph Suspensions of Even Cycles |
| topic | Combinatorics 05C65, 05C38 |
| url | https://arxiv.org/abs/2101.06743 |