Supersaturation for subgraph counts
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866910615248830464 |
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| author | Cutler, Jonathan Nir, JD Radcliffe, A. J. |
| author_facet | Cutler, Jonathan Nir, JD Radcliffe, A. J. |
| contents | The classic extremal problem is that of computing the maximum number of edges in an $F$-free graph. In the case where $F=K_{r+1}$, the extremal number was determined by Turán. Later results, known as supersaturation theorems, proved that in a graph containing more edges than the extremal number, there must also be many copies of $K_{r+1}$. Alon and Shikhelman introduced a broader class of problems asking for the maximum number of copies of a graph $T$ in an $F$-free graph. In this paper, we determine some of these generalized extremal numbers and prove supersaturation results for them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_08059 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Supersaturation for subgraph counts Cutler, Jonathan Nir, JD Radcliffe, A. J. Combinatorics The classic extremal problem is that of computing the maximum number of edges in an $F$-free graph. In the case where $F=K_{r+1}$, the extremal number was determined by Turán. Later results, known as supersaturation theorems, proved that in a graph containing more edges than the extremal number, there must also be many copies of $K_{r+1}$. Alon and Shikhelman introduced a broader class of problems asking for the maximum number of copies of a graph $T$ in an $F$-free graph. In this paper, we determine some of these generalized extremal numbers and prove supersaturation results for them. |
| title | Supersaturation for subgraph counts |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1903.08059 |