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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 581.10029

**Autor: ** Alon, Noga; Erdös, Pál

**Title: ** An application of graph theory to additive number theory. (In English)

**Source: ** Eur. J. Comb. 6, 201-203 (1985).

**Review: ** It is proved that, if {\frak A} = a_{1} < a_{2} < ... < a_{n} is a sequence of positive integers such that no integer can be expressed as a sum a_{i}+a_{j} in more than k ways, then {\frak A} is the union of C_{1}(k) n^{1/3} B_{2}-sequences, a B_{2}-sequence being a sequence with all two-element sums distinct. On the other hand, such an {\frak A} exists which is not the union of C_{2}(k) n^{1/3} B_{2}- sequences. Proofs are couched in terms of hypergraphs.

**Reviewer: ** I.Anderson

**Classif.: ** * 11B83 Special sequences of integers and polynomials

11P99 Additive number theory

05C65 Hypergraphs

**Keywords: ** Sidon sequence; distinct two-element sums; B_{2}-sequences; hypergraphs

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag