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The Analysis of a List-Coloring Algorithm on a Random Graph (extended abstract)
 

Summary: The Analysis of a List-Coloring Algorithm on a Random Graph
(extended abstract)
Dimitris Achlioptas*t
(optasQcs.toronto.edu1
Abstract
We introduce a natural k-coloring algorithm and
analyze its performance on random graphs with con-
stant expected degree c (Gn,p=c/n).For k = 3 our re-
sults imply that almost all graphs with n vertices and
1.923n edges are 3-colorable. This improves the lower
bound on the threshold for random 3-colorability sig-
nificantly and settles the last case of Q long-standing
open question of Bollobds [5]. We also provide a tight
asymptotic analysis of the algorithm. We show that
for all k 2 3, if c 5 klnk - 3/2k then the algorithm
almost surely succeeds, while for any E > 0, and k suf-
ficiently large, if c 2 (1+E)k In k then the algorithm
almost surely fails. The analysis is based on the use
of differential equations to approximate the mean path
of certain Markov chains.

  

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

 

Collections: Computer Technologies and Information Sciences