## Saturated $k$-Sperner Systems of Minimum Size ★★

Author(s): Morrison; Noel; Scott

**Question**Does there exist a constant and a function such that if , then every saturated -Sperner system has cardinality at least ?

Keywords: antichain; extremal combinatorics; minimum saturation; saturation; Sperner system

## List Colourings of Complete Multipartite Graphs with 2 Big Parts ★★

Author(s): Allagan

**Question**Given , what is the smallest integer such that ?

Keywords: complete bipartite graph; complete multipartite graph; list coloring

## Geometric Hales-Jewett Theorem ★★

**Conjecture**For all integers and , there is an integer such that for every set of at least points in the plane, if each point in is assigned one of colours, then:

- \item contains collinear points, or \item contains a monochromatic line (that is, a maximal set of collinear points receiving the same colour)

Keywords: Hales-Jewett Theorem; ramsey theory

## Generalised Empty Hexagon Conjecture ★★

Author(s): Wood

**Conjecture**For each there is an integer such that every set of at least points in the plane contains collinear points or an empty hexagon.

Keywords: empty hexagon