# geometric graph

## Circular colouring the orthogonality graph ★★

Author(s): DeVos; Ghebleh; Goddyn; Mohar; Naserasr

Let denote the graph with vertex set consisting of all lines through the origin in and two vertices adjacent in if they are perpendicular.

**Problem**Is ?

Keywords: circular coloring; geometric graph; orthogonality

## Coloring the Odd Distance Graph ★★★

Author(s): Rosenfeld

The *Odd Distance Graph*, denoted , is the graph with vertex set and two points adjacent if the distance between them is an odd integer.

**Question**Is ?

Keywords: coloring; geometric graph; odd distance

## Universal point sets for planar graphs ★★★

Author(s): Mohar

We say that a set is -*universal* if every vertex planar graph can be drawn in the plane so that each vertex maps to a distinct point in , and all edges are (non-intersecting) straight line segments.

**Question**Does there exist an -universal set of size ?

Keywords: geometric graph; planar graph; universal set