3 problems

Peng–Zhao's conjecture. The Lagrangian of $G$ satisfies

Let $r\geq 3$. An $r$-graph is linear if any two edges have at most one vertex in common, and it is lambda-perfect when its Lagrangian density equals the natural complete-hypergrap…

Let $r\geq 3$. An $r$-graph $G$ has $m$ edges and is lambda-perfect when its Lagrangian density equals the natural complete-hypergraph lower bound determined by its number of verti…