14 problems

Cubic-curve extremal conjecture. If $|B|=n$, then all points in $P\cup B$ lie on a cubic curve.

Let $q$ be a prime power satisfying $q\geq 13$ and $q\not\equiv 2\pmod 3$. A double blocking set in $\operatorname{PG}(2,q)$ is a set meeting every line in at least two points; a…

Szőnyi's conjecture. The blocking set $B$ has at least

Baer-subplane covering conjecture. If $\mathcal{L}$ covers every point of $\Pi_q$ outside $\Pi'$, then $\mathcal{L}$ is a covering set; in particular, it also covers every point of…

Let ${\mathscr C}$ be an ideal minimally non-packing clutter, meaning an ideal clutter that does not have the packing property but whose proper minors have the packing property. It…

Let $P$ be a $k$-blocked point set, with its points assigned one of $k$ colours so that two distinct points have the same colour exactly when some other point of $P$ blocks them. C…

A finite point set in the plane is $k$-blocked if its points are assigned one of $k$ colours such that two distinct points have the same colour exactly when some other point of the…

Let $b(n)$ be the minimum integer such that some set of $n$ points in the plane in general position is blocked by a set of $b(n)$ points. Superlinear blocker-number conjecture. … K…

For fixed $\ell$, let $b_\ell(n)$ be the minimum integer such that every set of $n$ points in the plane with no $\ell$ collinear points can be blocked by a set of $b_\ell(n)$ point…

A finite point set is in convex position if every point is a vertex of its convex hull. A blocker for such a set is a point, outside the set, lying on an edge segment determined by…

Let $t(n)$ be the minimum number of colours needed to colour the edges of some geometric drawing of $K_n$ so that every pair of edges with the same colour crosses; each colour clas…

Let $P$ be a set of points in the plane with at most $\frac{1}{2}|P|$ points collinear. Suppose that a set $B$ blocks $P$, meaning that for every two distinct points $x,y\in P$ the…

A drawing of a graph represents vertices by distinct plane points and edges by simple curves, with a vertex meeting an edge only at an endpoint. A drawing is simple if any two edge…

For a finite set $P$ of points in the plane, a set $B$ of points disjoint from $P$ blocks $P$ if every segment joining two distinct points of $P$ contains a point of $B$. If $P$ is…