All Questions

For a positive integer $n$, let $\mathcal{P}$ be the power set of $[n]$. Consider the graph $G$ with $\mathcal{P}$ as its vertex set, and, for $S_1,S_2 \in \mathcal{P}$, the edge $(S_1,S_2)$ exists ...

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(...

I'm not an expert in combinatorics, but it sometimes comes up in my research with students in computer science (which is already pretty far away from my speciality of abstract homotopy theory). I just ...