Lagrangian densities of short 3-uniform linear paths and Turán numbers of their extensions

Biao Wu, Yuejian Peng

For a fixed positive integer $n$ and an $r$-uniform hypergraph $H$, the Turán number $ex(n,H)$ is the maximum number of edges in an $H$-free $r$-uniform hypergraph on $n$ vertices,…