4 problems

Loom component conjecture. Then

Loom fractional covering conjecture. If $\mathbb{L}=(A,B)$ is an $(r,s)$-loom, then

Projective-plane extremal conjecture. For $m\geqslant r+2$,

Let $H$ be a hypergraph of separated $d$-intervals. Write $u(H)$ for its matching number and $\tau^(H)$ for its fractional covering number. Fractional covering conjecture. One shou…