Conjecture   Associahedra have unbounded chromatic number.

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)

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.

Question   Does there exist a -degenerate graph with chromatic number and girth , for all and ?

Conjecture   Every graph with average degree at least contains every 2-regular graph on vertices as a minor.

Conjecture   For every graph ,
(a)
(b)
(c) .

Conjecture   Every graph with minimum degree at least 7 contains a -minor.

Conjecture   Every 7-connected graph contains a -minor.

Problem   Classify the point sets with no empty pentagon.

Question   Is there a constant such that every -vertex -minor-free graph has at most cliques?

Conjecture   For all integers there is an integer such that every set of at least points in the plane contains at least collinear points or pairwise visible points.