Finite Graphs and the Number of Sums and Products

Xing- De Jia () and Melvyn B. Nathanson ()
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Xing- De Jia: Southwest Texas State University, Department of Mathematics
Melvyn B. Nathanson: Lehman College (CUNY), Department of Mathematics

Chapter 16 in Number Theory: New York Seminar 1991–1995, 1996, pp 211-219 from Springer

Abstract: Abstract Let G be a graph with k vertices (1, 2, …, k) and e edges. Let A = (α1,α2,..,α k ) be a set of k integers, and let G(A) be the set of all integers of the form α i + α j and α i α j , where (i,j) is an edge of G. Erdös and Szemerédi conjectured that |G(α)| ≫ ε e /k ε for every ε > 0 and every set A. This conjecture will be proved in the case that the diameter of the set A is polynomial in k.

Date: 1996
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DOI: 10.1007/978-1-4612-2418-1_16

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