Coloring plane graphs with independent crossings

We show that every plane graph with maximum face size four whose all faces of size four are vertex-disjoint is cyclically 5-colorable. This answers a question of Albertson whether graphs drawn in the plane with all crossings independent are 5-colorable.

• Type: Journal
• Year: 2010
• Where: JGT
• Authors: Daniel Král', Ladislav Stacho
• Keywords: JGT 2010, Maximum Face, Plane Graph