## The Analysis of a List-Coloring Algorithm on a Random Graph (Extended Abstract) (1997)

Citations: | 32 - 5 self |

### BibTeX

@MISC{Achlioptas97theanalysis,

author = {Dimitris Achlioptas and et al.},

title = {The Analysis of a List-Coloring Algorithm on a Random Graph (Extended Abstract)},

year = {1997}

}

### Years of Citing Articles

### OpenURL

### 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 1.923 n edges are 3-colorable. This improves the lower bound on the threshold for random 3-colorability significantly and settles the last case of Q long-standing open question of Bollobas [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 sufficiently 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.