A graph is a triple consisting of a vertex set , an edge set , and a relation which associates each of the edges with two vertices called it's endpoints. A complete graph is a simple graph whose vertices are pairwise adjacent; the complete graph with vertices is denoted . Graphs with a number of edges roughly quadratic in their number of vertices are usually called dense. In 1928, the English mathematician Frank Plumpton Ramsey published his paper on a problem of formal logic in which he proved what would become known as Ramsey’s Theorem. The paper has led to a large area of combinatorics now known as Ramsey Theory.