Abstract
For a graph F, we say a hypergraph is a Berge-F if it can be obtained from F by replacing each edge of F with a hyperedge containing it. A hypergraph is Berge-F-free if it does not contain a subhypergraph that is a Berge-F. The weight of a non-uniform hypergraph H is the quantity P h2E(H) jhj. Suppose H is a Berge-F-free hypergraph on n vertices. In this short note, we prove that as long as every edge of H has size at least the Ramsey number of F and at most o(n), the weight of H is o(n2). This result is best possible in some sense. Along the way, we study other weight functions, and strengthen results of Gerbner and Palmer; and Grosz, Methuku and Tompkins.
| Original language | English |
|---|---|
| Article number | P4.7 |
| Journal | Electronic Journal of Combinatorics |
| Volume | 26 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2019 |
Funding
∗Supported by the János Bolyai Research Fellowship of the Hungarian Academy of Sciences and by the National Research, Development and Innovation Office – NKFIH, grant SNN 116095, grant K 116769 and grant KH 130371. †Supported by IBS-R029-C1 and the National Research, Development and Innovation Office NKFIH grant K116769. ‡Supported by University of Montana UGP Grant #M25460.
| Funder number |
|---|
| SNN 116095, KH 130371, IBS-R029-C1 |
| K116769 |
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