<i>C</i>₁₀ Has Positive Turán Density in the Hypercube

ABSTRACT The ‐dimensional hypercube is a graph with vertex set such that there is an edge between two vertices if and only if they differ in exactly one coordinate. For any graph , define to be the maximum number of edges of a subgraph of without a copy of . In this short note, we prove that for any , where is the number of edges of . Our construction is strongly inspired by the recent breakthrough work of Ellis, Ivan, and Leader, who showed that ‘daisy’ hypergraphs have positive Turán density with an extremely clever and simple linear‐algebraic argument.