5 problems

Bollobás–Thomason threshold conjecture. The property $\mathcal{P}$ has a threshold in $\mathbb{G}(n,p\,; \,\binom{[n]}{k})$.

Let $\degree$ be a degree sequence, and let $\psi(\degree)$ denote the number of nonzero entries of the associated multigraph representation. Define $v(\degree)$ as the smallest re…

Consider the Markov chain defined by the edge-swap algorithm for the uniform model on dense multigraphs, and let $m$ denote the number of edges. Cubic-logarithmic mixing-time conje…

Let $\degree$ be a degree sequence, let $\beta$ denote the parameter associated with it, and let $u(\degree)$ be the constant bounding the effect of perturbations of $\degree$ on…

Let $h:\mathbb{R}^n\setminus\{\mathbf{0}\}\to\mathbb{R}^n$ be defined componentwise by … Let $\mathbf{J}$ be the Jacobian of $h$, and let … For $\boldsymbol{\beta}\in\mathcal{B}$,…