Un método algoritmo para el cálculo del número baricéntrico de Ramsey para el grafo estrella

Abstract

Let G be an abelian finite group and H be a graph. A sequence in G, with length al least two, is barycentric if it contains an ”average” element of its terms. Within the context of these sequences, one defines the barycentric Ramsey number, denoted by BR(H, G), as the smallest positive integer t such that any coloration of the edges of the complete graph Kt with elements of G produces a barycentric copy of the graph H. In this work we present a method based on the combinatorial theory and on the definition of barycentric Ramsey for calculating exact values of the above metioned constant, for some small graphs where the order is less than or equal to 8. We will exemplify the case where H is the star graph K1,k, and where G is the cyclical group Zn, with 3 ≤ n ≤ 11 and 3 ≤ k ≤ n.