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Balanced supersaturation for some degenerate hypergraphs

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Title
Balanced supersaturation for some degenerate hypergraphs
Author(s)
Corsten, Jan; Tuan Tran
Publication Date
2021-07
Journal
Journal of Graph Theory, v.97, no.4, pp.600 - 623
Publisher
John Wiley and Sons Inc
Abstract
© 2021 Wiley Periodicals LLCA 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.
URI
https://pr.ibs.re.kr/handle/8788114/10026
DOI
10.1002/jgt.22674
ISSN
0364-9024
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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