4 problems

Strengthened Alon–Wei conjecture. There exists an absolute constant $c>0$ such that for every $n,d\geq 2$, there is a spanning subgraph $H$ of $G$ satisfying

Concentration conjecture. The irregular random subgraph $H$ satisfies

Let $G$ be a graph on $n$ vertices with minimum degree $\delta$. For a graph $F$, let $m(F)$ denote the maximum number of vertices having the same degree in $F$. Bounded repeated-d…

Let $G$ be a $d$-regular graph on $n$ vertices. For a graph $F$ and a nonnegative integer $k$, let $m(F,k)$ denote the number of vertices of degree $k$ in $F$. Balanced degree-coun…