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Almost all graphs with 2.522n edges are not 3-colorable Dimitris Achlioptas
 

Summary: Almost all graphs with 2.522n edges are not 3-colorable
Dimitris Achlioptas
optas@cs.toronto.edu
Michael Molloy
molloy@cs.toronto.edu
Department of Computer Science
University of Toronto
Toronto, Ontario M5S 3G4, Canada.
Abstract
We prove that for c 2.522 a random graph with n vertices and m = cn edges
is not 3-colorable with probability 1 - o(1). Similar bounds for non-k-colorability are
given for k > 3.
1991 Mathematics Subject Classification: Primary 05C80; Secondary 05C15.
1 Introduction
Let N(n, m, A) denote the number of graphs with vertices {1, . . . , n}, m = m(n) edges and
some property A. The term "almost all" in the title has the meaning introduced by Erdos
and RŽenyi [5]:
lim
n
N(n, m, A)

  

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

 

Collections: Computer Technologies and Information Sciences