8 problems

Let $G(n,\alpha)$ be the random Borsuk graph in dimension $d$, and let $\chi(G(n,\alpha))$ denote its chromatic number. Logarithmic threshold conjecture. For every $d\geq 2$ there…

Let $G(n,\alpha)$ be the random Borsuk graph in dimension $d$, with chromatic number denoted by $\chi(G(n,\alpha))$. For a monotone graph property, a sharp threshold is a threshold…

Let $G(n,\alpha)$ be the random Borsuk graph in dimension $d$, let $\chi(G(n,\alpha))$ denote its chromatic number, and let $\alpha_0$ be the constant supplied by the Erdős–Hajnal…

Let $G(n,\alpha)$ be the random Borsuk graph in dimension $d$, and let $\chi(G(n,\alpha))$ denote its chromatic number. Polynomial threshold conjecture. For each $d\geq 2$, there e…

Random generalized Borsuk graph threshold conjecture. There exist constants $C_k$, $\overline{C}_k$ and functions $f_k:\mathbb{N}\to\mathbb{R}^+$ such that, if

Strict-growth conjecture. For all $d\geq 0$,

Cyclic-group Borsuk covering conjecture.

Generalized Borsuk covering-number conjecture.