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Extremal numbers for cycles in a hypercube
Published 23 Nov 2022 in math.CO | (2211.12842v2)
Abstract: Let $ex(Q_n, H)$ be the largest number of edges in a subgraph $G$ of a hypercube $Q_n$ such that there is no subgraph of $G$ isomorphic to $H$. We show that for any integer $k\geq 3$, $$ex(Q_n, C_{4k+2})= O(n{\frac{5}{6} + \frac{1}{3(2k-2)}} 2n).$$
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