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Maximal number of perfect matchings that pairwise form a Hamiltonian cycle
Definition: Let $MH(n)$ be the maximal number of perfect matchings (1-regular graphs) on $n$ vertices where the union of any two perfect matchings is a Hamiltonian cycle.
Question: Is it true that $MH(...
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Turán density of hypergraphs with very few edges
As usual, for an $r$-uniform hypergraph $G$, denote by $ex_r(n,G)$ the maximum number of edges an $r$-uniform, $G$-free hypergraph on $n$ vertices can have, and let $\lim \frac{ex_r(n,G)}{\binom nr}\...
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