### Abstract

A sequence of integers A = {a_{1} < a_{2} < ⋯ < a_{n}} is a B^{k}_{2} sequence if the number of representations of every integer as the sum of two distinct a_{i}s is at most k. In this note we show that every B^{k}_{2} sequence of n terms is a union of c^{k}_{2} · n^{1/3}B^{1}_{2} sequences, and that there is a B^{k}_{2} sequence of n terms which is not a union of c^{k}_{1} · c^{1/3}B^{1}_{2} sequences. This solves a problem raised in [3, 4]. Our proof uses some results from extremal graph theory. We also discuss some related problems and results.

Original language | English (US) |
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Pages (from-to) | 201-203 |

Number of pages | 3 |

Journal | European Journal of Combinatorics |

Volume | 6 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1985 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics

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## Cite this

Alon, N. M., & Erdös, P. (1985). An Application of Graph Theory to Additive Number Theory.

*European Journal of Combinatorics*,*6*(3), 201-203. https://doi.org/10.1016/S0195-6698(85)80027-5