Ramsey theory
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Ramsey Theory is a branch of Graph theory which studies seemingly orderless systems and analyses the conditions under which order must be present. Typically it makes statements about the existence of specific sub-graphs in arbitrary graphs.
Ramsey Numbers
The Ramsey Number is defined as the least integer n such that whenever the complete graph is coloured, such that each edge is one of two colours, it contains either a with all edges the first colour, or a with all edges the second colour, if such an n exists.
Ramsey Numbers are rarely calculated, largely due to the rate at which the complexity of verifying the results grows.
Ramsey's Theorem
Ramsey's Theorem states that exists