6 problems

Let $R=\{(\alpha,\beta,\gamma)\in[0,1]^3:\alpha\beta+\gamma>1,\alpha\gamma+\beta>1,\beta\gamma+\alpha>1\}$, and let … Define…

The density domination exponent conjecture.

Degenerate-graph density conjecture. For every fixed $k$-degenerate graph $H$,

Let $H$ be a graph with edge densities $b3_e$. For each proper labeling $f$, consider the weighted monotone-path tree $T_f(H)$, with the edge weights interpreted as densities, and…

Skew blow-up conjecture. There is a constant $c>0$ such that

Balanced blow-up conjecture. For every $t\geq 2$,