# Wood, David R.

## Forcing a $K_6$-minor ★★

Author(s): Barát ; Joret; Wood

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

Keywords: connectivity; graph minors

## Point sets with no empty pentagon ★

Author(s): Wood

Problem   Classify the point sets with no empty pentagon.

Keywords: combinatorial geometry; visibility graph

## Number of Cliques in Minor-Closed Classes ★★

Author(s): Wood

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

Keywords: clique; graph; minor

## Compatible Matching Conjecture ★★

Author(s): Wood

For an even set of points in the plane, a perfect matching of is a collection of nonintersecting segments such that every point of is an end of exactly one of the segments.

Conjecture   Let be a set of points in the plane in general position such that is divisible by 4. Then for every perfect matching of there is another perfect matching, , of such that no segment of crosses a segment of .

Keywords: geometric graphs; matchings

## Big Line or Big Clique in Planar Point Sets ★★

Author(s): Kara; Por; Wood

Let be a set of points in the plane. Two points and in are visible with respect to if the line segment between and contains no other point in .

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.