Graphs on Affine and Linear Spaces and Deuber Sets
Keywords: Ramsey theory, independent sets, partition regular systems of equations
AbstractIf $G$ is a large $K_k$-free graph, by Ramsey's theorem, a large set of vertices is independent. For graphs whose vertices are positive integers, much recent work has been done to identify what arithmetic structure is possible in an independent set. This paper addresses similar problems: for graphs whose vertices are affine or linear spaces over a finite field, and when the vertices of the graph are elements of an arbitrary Abelian group.