# Maximum Hypergraphs without Regular Subgraphs

Jaehoon Kim; Alexandr V. Kostochka

Discussiones Mathematicae Graph Theory (2014)

- Volume: 34, Issue: 1, page 151-166
- ISSN: 2083-5892

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topJaehoon Kim, and Alexandr V. Kostochka. "Maximum Hypergraphs without Regular Subgraphs." Discussiones Mathematicae Graph Theory 34.1 (2014): 151-166. <http://eudml.org/doc/268219>.

@article{JaehoonKim2014,

abstract = {We show that an n-vertex hypergraph with no r-regular subgraphs has at most 2n−1+r−2 edges. We conjecture that if n > r, then every n-vertex hypergraph with no r-regular subgraphs having the maximum number of edges contains a full star, that is, 2n−1 distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n > r cannot be weakened.},

author = {Jaehoon Kim, Alexandr V. Kostochka},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {hypergraphs; set system; subgraph; regular graph},

language = {eng},

number = {1},

pages = {151-166},

title = {Maximum Hypergraphs without Regular Subgraphs},

url = {http://eudml.org/doc/268219},

volume = {34},

year = {2014},

}

TY - JOUR

AU - Jaehoon Kim

AU - Alexandr V. Kostochka

TI - Maximum Hypergraphs without Regular Subgraphs

JO - Discussiones Mathematicae Graph Theory

PY - 2014

VL - 34

IS - 1

SP - 151

EP - 166

AB - We show that an n-vertex hypergraph with no r-regular subgraphs has at most 2n−1+r−2 edges. We conjecture that if n > r, then every n-vertex hypergraph with no r-regular subgraphs having the maximum number of edges contains a full star, that is, 2n−1 distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n > r cannot be weakened.

LA - eng

KW - hypergraphs; set system; subgraph; regular graph

UR - http://eudml.org/doc/268219

ER -

## References

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