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http://www.elsevier.com/locate/jcss Journal of Computer and System Sciences 67 (2003) 441471
 

Summary: http://www.elsevier.com/locate/jcss
Journal of Computer and System Sciences 67 (2003) 441471
Almost all graphs with average degree 4 are 3-colorable
Dimitris Achlioptasa
and Cristopher Mooreb,c,,1
a
Microsoft Research, Redmond, Washington, USA
b
Computer Science Department, University of New Mexico, Farris Engineering Center, Albuquerque, NM 87131, USA
c
Santa Fe Institute, Santa Fe, NM, USA
Received 14 July 2002; revised 28 December 2002
Abstract
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., Gn; 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.
Keywords: Random graphs; Regular random graphs; Graph coloring; Threshold phenomena
1. Introduction
Let Gn; p be a random graph on n vertices where each edge appears independently of all

  

Source: Achlioptas, Dimitris - Department of Computer Engineering, University of California at Santa Cruz

 

Collections: Computer Technologies and Information Sciences