3 problems

Let $H$ be a hypergraph of $d$-intervals. Let $\chi_e(H)$ denote its edge chromatic number, and let $\Delta$ be the maximum degree of a point on any line. Edge-colouring conjecture…

Let $H$ be a hypergraph of $d$-intervals, let $\tau_w(H)$ be its weighted covering number, and let $\nu_w(H)$ be its weighted matching number. Weighted covering conjecture. One sho…

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…