Volume 32 • Number 1 • 2009   • Barycentric Ramsey Numbers for Small Graphs Samuel González, Leida González and Oscar Ordaz Abstract. Let be a finite abelian group of order . The barycentric Ramsey number is the minimum positive integer such that any coloring of the edges of the complete graph by elements of contains a subgraph whose assigned edge color constitutes a barycentric sequence, i.e. there exists one edge whose color is the “average” of the colors of its edges. These are determined for some graphs, in particular for graphs with at most four edges without isolated vertices (i.e. small graphs) and , . Elementary combinatorial arguments are used for these computations. 2000 Mathematics Subject Classification: 11B50, 11P70, 11B75. Full text: PDF