Zero-sum Ramsey number for non-cyclic group

Abstract:

Let G be a graph with n edges and let H be a finite abelian group such that the order of each element of H divides n. Let R(G,H) denote the minimum integer t such that for every function f: E(K<inf>t</inf>) → H there is a copy of G in K<inf>t</inf> with the property that (Formula Presented). We prove that for a positive integer r, if H = Z^r<inf>n</inf> is the abelian group of all vectors of length r over Z<inf>n</inf>, then R(G, 2^r) ≤ R(G,Z^r<inf>n</inf>), (0.1) where R(G, 2^r) is the smallest integer N such that for every 2^r-coloring of the edges of the complete graph K<inf>N</inf>, there is a monochromatic copy of G. Moreover, we shall consider the bounds to R(G,Z^r<inf>n</inf>) when G the star of n edges

Año de publicación:

2022

Keywords:

• STARS
• Ramsey numbers
• Zero-sum

Fuente:

scopus

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