Corsten, Jan and Tran, Tuan (2021) Balanced supersaturation for some degenerate hypergraphs. Journal of Graph Theory, 97 (4). pp. 600-623. ISSN 0364-9024
Full text not available from this repository.Abstract
A classical theorem of Simonovits from the 1980s asserts that every graph (Formula presented.) satisfying (Formula presented.) must contain (Formula presented.) copies of (Formula presented.). Recently, Morris and Saxton established a balanced version of Simonovits' theorem, showing that such (Formula presented.) has (Formula presented.) copies of (Formula presented.), which are “uniformly distributed” over the edges of (Formula presented.). Moreover, they used this result to obtain a sharp bound on the number of (Formula presented.) -free graphs via the method of hypergraph containers. In this article, we generalise Morris–Saxton's results for even cycles to (Formula presented.) -graphs. We also prove analogous results for complete (Formula presented.) -partite (Formula presented.) -graphs.
| Item Type: | Article |
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| Additional Information: | Funding Information: This study was motivated by a series of lectures of Rob Morris at the Ramsey DocCourse programme in Prague 2016. The authors would like to thank him and the organisers of the course, Jaroslav Nešetřil and Jan Hubička. Furthermore, the authors would like to thank Peter Allen for his helpful comments on this text, and Joonkyung Lee for pointing out the Reference [ 27 ]. The authors appreciate suggestions from two anonymous referees which helped improve the exposition of the paper. This study was supported by the Institute for Basic Science (IBS‐R029‐Y1). Much of the work was done while supported by the Czech Science Foundation, grant number GJ16‐07822Y, and with institutional support RVO:67985807, while affiliated with the Institute for Computer Science, Czech Academy of Sciences. Publisher Copyright: © 2021 Wiley Periodicals LLC Copyright: Copyright 2021 Elsevier B.V., All rights reserved. |
| Divisions: | Mathematics LSE Health |
| Date Deposited: | 03 May 2024 10:39 |
| Last Modified: | 16 May 2024 03:24 |
| URI: | http://eprints.lse.ac.uk/id/eprint/122889 |
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