### Abstract

A two-coloring of the vertices X of the hypergraph H=(X, ε) by red and blue has discrepancy d if d is the largest difference between the number of red and blue points in any edge. A two-coloring is an equipartition of H if it has discrepancy 0, i.e., every edge is exactly half red and half blue. Let f(n) be the fewest number of edges in an n-uniform hypergraph (all edges have size n) having positive discrepancy. Erdo{combining double acute accent}s and Sós asked: is f(n) unbounded? We answer this question in the affirmative and show that there exist constants c_{ 1} and c_{ 2} such that {Mathematical expression} where snd(x) is the least positive integer that does not divide x.

Original language | English (US) |
---|---|

Pages (from-to) | 151-160 |

Number of pages | 10 |

Journal | Combinatorica |

Volume | 7 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 1987 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Computational Mathematics

## Fingerprint Dive into the research topics of 'The smallest n-uniform hypergraph with positive discrepancy'. Together they form a unique fingerprint.

## Cite this

*Combinatorica*,

*7*(2), 151-160. https://doi.org/10.1007/BF02579446