3 problems

Let $n\geq 3$. For an $n$-dimensional convex body $K$, let $I(K)$ be the smallest number of directions that illuminate every point of the boundary of $K$, and let $H(n)$ be the max…

Gyárfás's conjecture. For fixed $k$, there exist sets $A_1,A_2,\dots,A_{k-1}$ whose union is $[n]$, and colours $c_1,c_2,\dots,c_{k-1}$, such that $K_n[A_i,c_i]$ is connected for e…

Ryser–Lovász conjecture. For every integer $r\geq 2$ and every graph $G$,