Two-regular subgraphs of odd-uniform hypergraphs

Jie Han; Jaehoon Kim

doi:10.1016/j.jctb.2017.08.009

Two-regular subgraphs of odd-uniform hypergraphs

Jie Han, Jaehoon Kim

University of Birmingham

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Let k≥3 be an odd integer and let n be a sufficiently large integer. We prove that the maximum number of edges in an n-vertex k-uniform hypergraph containing no 2-regular subgraphs is (n−1k−1)+⌊[Formula presented]⌋, and the equality holds if and only if H is a full k-star with center v together with a maximal matching omitting v. This verifies a conjecture of Mubayi and Verstraëte.

Original language	English
Pages (from-to)	175-191
Number of pages	17
Journal	Journal of Combinatorial Theory. Series B
Volume	128
DOIs	https://doi.org/10.1016/j.jctb.2017.08.009
Publication status	Published - Jan 2018
Externally published	Yes

Keywords

Hypergraph
Regular graph
Regular subgraph
Subgraph

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10.1016/j.jctb.2017.08.009

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Han, J., & Kim, J. (2018). Two-regular subgraphs of odd-uniform hypergraphs. Journal of Combinatorial Theory. Series B, 128, 175-191. https://doi.org/10.1016/j.jctb.2017.08.009

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AB - Let k≥3 be an odd integer and let n be a sufficiently large integer. We prove that the maximum number of edges in an n-vertex k-uniform hypergraph containing no 2-regular subgraphs is (n−1k−1)+⌊[Formula presented]⌋, and the equality holds if and only if H is a full k-star with center v together with a maximal matching omitting v. This verifies a conjecture of Mubayi and Verstraëte.

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KW - Regular subgraph

KW - Subgraph

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ER -

Two-regular subgraphs of odd-uniform hypergraphs

Abstract

Keywords

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