Regular subgraphs of uniform hypergraphs

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We prove that for every integer r >= 2, an n-vertex k-uniform hypergraph H containing no r-regular subgraphs has at most (1 + o(1)) [GRAPHICS] edges if k >= r + 1 and n is sufficiently large. Moreover, if r is an element of {3, 4}, r vertical bar k and k, n are both sufficiently large, then the maximum number of edges in an n-vertex k-uniform hypergraph containing no r-regular subgraphs is exactly [GRAPHICS] , with equality only if all edges contain a specific vertex v. We also ask some related questions. (C) 2016 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2016-07
Language
English
Article Type
Article
Citation

JOURNAL OF COMBINATORIAL THEORY SERIES B, v.119, pp.214 - 236

ISSN
0095-8956
DOI
10.1016/j.jctb.2016.03.001
URI
http://hdl.handle.net/10203/263345
Appears in Collection
MA-Journal Papers(저널논문)
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