8 problems

Biconnected graph Jacobian order conjecture. Fix a vertex $x$. Then there exists a vertex $y$ such that

Existential generator conjecture.

Fixed-pair generator probability conjecture. For each graph, fix vertices $x$ and $y$. Then

Let $n$ be a positive integer, and let $k_n$ be an integer depending on $n$. A graph is biconnected if it has the connectivity property intended in the paper. Bounded multiplicity…

Let $\mathcal{E}_{2^r}$ denote the exceptional pairing on the cyclic group of order $2^r$, as used in the paper. For an integer $k\geq 1$, consider the direct product of $k$ copies…

Let $G$ be a finite graph, and let $\Gamma=\operatorname{Jac}(G)$ be its Jacobian, equipped with its canonical monodromy pairing … For a finite abelian group with pairing…

Let $G(n,q)$ be the Erdős–Rényi random graph on $n$ vertices, with each edge included independently with fixed probability $0<q<1$. The cyclicity probability conjecture. The probab…

Let $G(n,q)$) be the Erdős–Rényi random graph on $n$ vertices, with each edge included independently with fixed probability $0<q<1$. Let $\Gamma(n,q)={\operatorname{Jac}}(G(n,q))$,…