Topology of Cayley Graphs Applied to Inverse Additive Problems

2010/11/08 by Yahya Ould Hamidoune, Hamidoune, Yahya Ould
Computer Science · Mathematics · #11B34 #11B60 #20D60 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1011.1797

openalex publication_date 2010/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We present proofs of the basic isopermetric structure theory, obtaining some new simplified proofs. As an application, we obtain simple descriptions for subsets S of an abelian group with |kS|≤ k|S|-k+1 or |kS-rS|- (k+r)|S|, where 1≤ r ≤ k. These results may be applied to several questions in Combinatorics and Additive Combinatorics (Frobenius Problem, Waring's problem in finite fields and Cayley graphs with a big diameter, ....).

Citations

• Hyper-atoms and the critical pair Theory
• A Structure Theory for Small Sum Subsets

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