A lower bound on the hypergraph Ramsey number R(4,5;3)
The finite version of Ramsey's theorem says that for positive integers r, k, a_1,... ,a_r, there exists a least number n=R(a_1, \ldots, a_r; k) so that if X is an n-element set and all k-subsets of X are r-coloured, then there exists an i and an a_i-set A so that all k-subsets of A are coloured with the ith colour.
In this paper, the bound R(4, 5; 3) >= 35 is shown by using a SAT solver to construct a red--blue colouring of the triples chosen from a 34-element set.
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