Almost all graphs with average degree 4 are 3-colorable

We analyze a randomized version of the Brelaz heuristic on sparse random graphs. We prove that almost all graphs with average degree dp4:03; i.e., G?n; p ? d=n?; are 3-colorable and that a constant fraction of all 4-regular graphs are 3-colorable. r 2003 Elsevier Inc. All rights reserved.

• Type: Conference
• Year: 2002
• Where: STOC
• Authors: Dimitris Achlioptas, Cristopher Moore
• Keywords: 4-regular Graphs, Algorithms, Sparse Random Graphs, STOC 2002