The dynamics of proving uncolourability of large random graphs I. Symmetric Colouring Heuristic

Details The dynamics of proving uncolourability of large random graphs I. Symmetric Colouring Heuristic The dynamics of proving uncolourability of large random graphs I. Symmetric Colouring Heuristic

2003-04-28

arxiv.org/abs/cond-mat/0304606v1

Physics

Condensed Matter

Statistical Mechanics

5 figures

Scientific paper

10.1088/0305-4470/36/43/027

We study the dynamics of a backtracking procedure capable of proving uncolourability of graphs, and calculate its average running time T for sparse random graphs, as a function of the average degree c and the number of vertices N. The analysis is carried out by mapping the history of the search process onto an out-of-equilibrium (multi-dimensional) surface growth problem. The growth exponent of the average running time is quantitatively predicted, in agreement with simulations.

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