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

Liat Ein-Dor·Remi Monasson
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Abstract

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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Liat Ein-Dor, Remi Monasson. 2003-04-28. The dynamics of proving uncolourability of large random graphs I. Symmetric Colouring Heuristic. https://doi.org/10.1088/0305-4470%2F36%2F43%2F027

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