2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74705We present an elementary proof that if $A$ is a finite set of numbers, and the sumset $A+_GA$ is small, $|A+_GA|\leq c|A|$, along a dense graph $G$, then $A$ contains $k$-term arithmetic progressions.To appear in Combinatorics Probability and ComputationNumber TheoryCombinatorics11P70text