The Ramsey numbers with components H-good and simultaneous sequences

• José Figueroa Departamento de Qumica, Universidad Clodosbaldo Russián
• Felicia Villarroel Departamento de Matemática Universidad de Oriente
• Henry Ramı́rez Departamento de Higiene y Seguridad Laboral, Universidad Clodosbaldo Russián
• Juan Otero Departamento de Informática, Universidad Clodosbaldo Russián

Keywords: combinatory theory, set of symmetric sequences, sequences k-baricentric sequences

Abstract

Given two graphs $G$ and $H$ do not empty. The number of Ramsey $R(G,H)$ is defined as the minor positive integer $n$, such that for some graph $F$ wich containing a monochromatic copy $G^{'}$ isomorphic to $G$ or the complement of $F$, contains a monochromatic copy $H^{'}$ isomorphic to $H$. In this work, we present a method based on the combinatorial theory, and the definition of linear forest, to determine a set $W$ of sequences with $m+1$ elements of size $m$ each one, with each sequence $s_{i}$ the sides of the minor complete graphs $K_{n}=F\cup\overline{F}$ are colored. In second place, the demonstration of the theorem wich result of the combination of the graphs: wheel $W_{n}$ for $n\geq 5$ and diamond is done. In this case, we prove that the Ramsey number is $R(G;H)=n+1$, furthermore we prove the symmetry and $k$-baricentricity monochromatic of the set of sequences.

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