Probabilistic graph colouring algorithms using Zykov trees
Date
1986
Authors
Lepolesa, Pikie M.
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Abstract
Let G=(V ,E) be a simple, undirected graph. A colouring of G is a mapping c : V ➔ {1,2, ... ,k}. c is a proper colouring if c(u) * c(v) for all {u,v} in E. The chromatic number of G, denoted x (G), is the smallest positive integer k for which a proper k-colouring exists. The graph colouring decision problem is to determine whether for a graph G and a positive integer k, there exists a proper colouring of G using at most k colours. A Las Vegas algorithm, i.e. a probabilistic algorithm that never lies, for the graph colouring decision problem that runs in polynomial time on almost all instances of the problem is given. Experimental results obtained with this algorithm suggest that it works well for sparse graphs. An approximation algorithm is suggested for graph colouring optimisation problem.