Barycentric sequences and barycentric Ramsey numbers stars Original Research Article

Let G be a finite abelian group. In the context of barycentric sequences, the barycentric Ramsey number of graphs is introduced. It is the minimum positive integer r such that any coloring of the edges of the complete graph Kr by elements of G yields a copy of a given graph containing one edge whose color is the “average” of the colors of its edges. The k-barycentric Davenport constant BD(k,G) is introduced and some values or bounds are given. In particular, these results allow to establish barycentric Ramsey numbers for stars.