Ramsey's Theorem states that for every positive integers say k1 and k2, there exists an integer R(k1, k2) known as ramsey number, such that any graph with R(k1, k2) nodes contain a clique with atleast 'k1' nodes or independent set with atleast 'k2' nodes.

Ramsey's Theorem states that for every positive integers say k1 and k2, there exists an integer R(k1, k2) known as ramsey number, such that any graph with R(k1, k2) nodes contain a clique with atleast 'k1' nodes or independent set with atleast 'k2' nodes.

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The online proof of ** Ramsey's Number Theorem** is made easier here.