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We show that the quantum query complexity of detecting if an n-vertex graph contains a triangle is O(n^9/7). This improves the previous best algorithm of Belovs making O(n^35/27) queries. For the problem of determining if an operation ∘ : S × S → S is associative, we give an algorithm making O(|S|^10/7) queries, the first improvement to the trivial O(|S|^3/2) application of Grover search. Our algorithms are designed using the learning graph framework of Belovs. We give a family of algorithmsarXiv:1210.1014v1 fatcat:57t2dmwmm5bbfo3ejdvahgcak4