# planar

## Degenerate colorings of planar graphs ★★★

Author(s): Borodin

A graph is -*degenerate* if every subgraph of has a vertex of degree .

**Conjecture**Every simple planar graph has a 5-coloring so that for , the union of any color classes induces a -degenerate graph.

Keywords: coloring; degenerate; planar

## The Two Color Conjecture ★★

Author(s): Neumann-Lara

**Conjecture**If is an orientation of a simple planar graph, then there is a partition of into so that the graph induced by is acyclic for .