Hamidoune, Yahya Ould Subsets with small sums in abelian groups. I: The Vosper property. (English) Zbl 0883.05065 Eur. J. Comb. 18, No. 5, 541-556 (1997). This paper characterizes the finite subsets \(B\) in an abelian group \(G\) such that, for any finite subset \(A\) having at least two elements, \(|A + B|\geq\) min\((|G|-1, |A|+|B|)\). The approach uses graph-theoretic ideas on Cayley graphs, including the concepts of “fragments” and “atoms” in a graph (as in H. A. Jung [Math. Ann. 202, 307-320 (1973; Zbl 0239.05133)]). Applications are given to diagonal forms over finite fields and to characterizing Cayley graphs (or loop networks) of high connectivity. Reviewer: A.J.Goodman (Rolla) Cited in 1 ReviewCited in 26 Documents MSC: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C40 Connectivity 20D60 Arithmetic and combinatorial problems involving abstract finite groups Keywords:abelian group; Cayley graph; connectivity; fragment; atom Citations:Zbl 0239.05133 PDFBibTeX XMLCite \textit{Y. O. Hamidoune}, Eur. J. Comb. 18, No. 5, 541--556, ej950113 (1997; Zbl 0883.05065) Full Text: DOI