# planar graph

## Bounded colorings for planar graphs ★★

Author(s): Alon; Ding; Oporowski; Vertigan

**Question**Does there exists a fixed function so that every planar graph of maximum degree has a partition of its vertex set into at most three sets so that for , every component of the graph induced by has size at most ?

Keywords: coloring; partition; planar graph

## 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

## What is the largest graph of positive curvature? ★

**Problem**What is the largest connected planar graph of minimum degree 3 which has everywhere positive combinatorial curvature, but is not a prism or antiprism?

Keywords: curvature; planar graph