Random Graph Coloring - a Statistical Physics Approach

Details Random Graph Coloring - a Statistical Physics Approach Random Graph Coloring - a Statistical Physics Approach

2002-07-18

arxiv.org/abs/cond-mat/0207453v1

Physics

Condensed Matter

Statistical Mechanics

17 pages, 9 figures

Scientific paper

10.1103/PhysRevE.66.056120

The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte-Carlo simulations. We critically discuss the merits and shortcomings of the various methods, and interpret the results obtained. We present an exact analytical expression for the 2-coloring problem as well as general replica symmetric approximated solutions for the thermodynamics of the graph coloring problem with p colors and K-body edges.

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