Coloring squares of planar graphs with girth six

Wang and Lih conjectured that for every g 5, there exists a number M(g) such that the square of a planar graph G of girth at least g and maximum degree M(g) is (+1)-colorable. The conjecture is known to be true for g 7 but false for g {5, 6}. We show that the conjecture for g = 6 is off by just one, i.e., the square of a planar graph G of girth at least six and sufficiently large maximum degree is ( + 2)-colorable.

• Type: Journal
• Year: 2008
• Where: EJC
• Authors: Zdenek Dvorak, Daniel Král, Pavel Nejedlý, Riste Skrekovski
• Keywords: Conjecture, EJC 2007, EJC 2008, Information Technology, Planar Graph, Wang