The structure of sets with few sums along a graph

摘要

We present common generalizations of some structure results of Freiman, Ruzsa, Balog-Szemeredi and Laczkovich-Ruzsa. We also give some applications to Combinatorial Geometry and Algebra, some of which generalize the aforementioned structure results even further. (c) 2006 Elsevier Inc. All rights reserved.