6 problems

Berge–Füredi conjecture. A linear (loopless) hypergraph $(V,E)$ satisfies

A $3$-graph $F$ is linear if any two of its edges share at most one vertex. For fixed $F$, let $r(F,K_n^{(3)})$ be the least $N$ such that every red-blue coloring of $K_N^{(3)}$ co…

A 3-uniform hypergraph is linear if any two of its edges intersect in at most one vertex. Linear-subhypergraph conjecture. There is a constant $c>0$ such that for every integer…

Let $F$ be an $r$-uniform hypergraph and let $k$ be the uniformity of the clique $K_{k+1}^k$. Distinct edges of $F$ satisfy the $k$-linear condition when $|e\cap f|<k$ for every pa…

Defective-colouring conjecture. Every $(r+1)$-uniform linear hypergraph with maximum degree at most $\Delta$ has a $d$-defective colouring with

Dual Erdős–Faber–Lovász conjecture. Any linear hypergraph on $n$ vertices has chromatic index at most $n$.