In graph theory, an Andrásfai graph is a triangle-free, circulant graph named after Béla Andrásfai.

The Andrásfai graph And(n) for any natural number n ≥ 1 is a circulant graph on 3n – 1 vertices, in which vertex k is connected by an edge to vertices k ± j, for every j that is congruent to 1 mod 3.

The graph family is triangle-free, and And(n) has an independence number of n. From this the formula R(3,n) ≥ 3(n – 1) results, where R(n,k) is the Ramsey number.

The Andrásfai graphs were later generalized.

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