5 problems

Let $k\geq 2$ be an integer, let $\lambda\geq 1$, and let a $k$-uniform linear hypergraph be a hypergraph in which every edge has $k$ vertices and any two distinct edges intersect…

Let $d(r,n)$ be the smallest average degree such that every $n$-vertex graph with average degree at least $d(r,n)$ contains an $r$-regular subgraph. Quadratic-logarithmic conjectur…

Let $s\geq 3$ be an integer and let $\varepsilon>0$. Bounded-size regular-subgraph conjecture. There is a positive integer $t$ such that, for all sufficiently large $n$, every $n$-…

Let $s\geq 3$ be an integer. For sufficiently large $n$, let $G$ be an $n$-vertex graph with average degree at least $d$, where $C\log\log n\leq d\leq n^{\frac{s-2}{s}}$. Regular-s…

Let $k\geq 3$ be an integer. An $n$-vertex $k$-uniform hypergraph is said to have no $2$-regular subgraphs on $2k$ vertices if it contains no subhypergraph on exactly $2k$ vertices…