
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
