The term r(4,4) refers to a specific Ramsey number which denotes the minimum number of vertices needed in a complete graph to ensure that either a clique of size 4 or an independent set of size 4 must exist. This concept is essential in understanding the relationships between cliques and independent sets, as well as in determining the bounds and known values associated with Ramsey numbers. Essentially, r(4,4) helps to illuminate the connections between combinatorial structures and the guarantees provided by Ramsey theory.
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