### Abstract

A set T is said to cover a set system J if T meets all members of J. We raise the following general problem. Find relations among the natural numbers p, r, s, t, that imply the truth of the following statement: If J. is an r-uniform set system such that each of its subsystems on at most p elements can be covered with an s-element set, then J. can be covered with a t-element set. Here we investigate the case s = 1.

Original language | English |
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Pages (from-to) | 78-84 |

Number of pages | 7 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 58 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1991 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory, Series A*,

*58*(1), 78-84. https://doi.org/10.1016/0097-3165(91)90074-Q

**Local constraints ensuring small representing sets.** / Erdős, P.; Hajnal, András; Tuza, Z.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory, Series A*, vol. 58, no. 1, pp. 78-84. https://doi.org/10.1016/0097-3165(91)90074-Q

}

TY - JOUR

T1 - Local constraints ensuring small representing sets

AU - Erdős, P.

AU - Hajnal, András

AU - Tuza, Z.

PY - 1991

Y1 - 1991

N2 - A set T is said to cover a set system J if T meets all members of J. We raise the following general problem. Find relations among the natural numbers p, r, s, t, that imply the truth of the following statement: If J. is an r-uniform set system such that each of its subsystems on at most p elements can be covered with an s-element set, then J. can be covered with a t-element set. Here we investigate the case s = 1.

AB - A set T is said to cover a set system J if T meets all members of J. We raise the following general problem. Find relations among the natural numbers p, r, s, t, that imply the truth of the following statement: If J. is an r-uniform set system such that each of its subsystems on at most p elements can be covered with an s-element set, then J. can be covered with a t-element set. Here we investigate the case s = 1.

UR - http://www.scopus.com/inward/record.url?scp=0009890598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009890598&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(91)90074-Q

DO - 10.1016/0097-3165(91)90074-Q

M3 - Article

AN - SCOPUS:0009890598

VL - 58

SP - 78

EP - 84

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 1

ER -