## 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} = a1 < a2 < ... < an is a sequence of positive integers such that no integer can be expressed as a sum ai+aj in more than k ways, then {\frak A} is the union of C1(k) n1/3 B2-sequences, a B2-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 C2(k) n1/3 B2- sequences. Proofs are couched in terms of hypergraphs.
Reviewer:  I.Anderson
Classif.:  * 11B83 Special sequences of integers and polynomials