An Upper Bound for the Ramsey Numbers
نویسندگان
چکیده
The Ramsey number r(H,G) is defined as the minimum N such that for any coloring of the edges of the N -vertex complete graph KN in red and blue, it must contain either a red H or a blue G. In this paper we show that for any graph G without isolated vertices, r(K3, G) ≤ 2q + 1 where G has q edges. In other words, any graph on 2q + 1 vertices with independence number at most 2 contains every (isolate-free) graph on q edges. This establishes a 1980 conjecture of Harary. The result is best possible as a function of q.
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