An Õ(n3/14)-coloring algorithm for 3-colorable graphs
Information Processing Letters
A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM Journal on Computing
The complexity of counting colourings and independent sets in sparse graphs and hypergraphs
Computational Complexity
Systematic Generation of Very Hard Cases for Graph 3-Colorability
TAI '95 Proceedings of the Seventh International Conference on Tools with Artificial Intelligence
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
3-coloring in time O (1.3289n)
Journal of Algorithms
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The 3-Colouring of a graph is a classic NP-complete problem. We show that some solutions for the 3-Colouring can be built in polynomial time based on the number of basic cycles existing in the graph. For this, we design a reduction from proper 3-Colouring of a graph G to a 2-CF Boolean formula FG, where the number of clauses in FG depends on the number of basic cycles in G. Any model of FG provides a proper 3-Colouring of G. Thus, FG is a logical pattern whose models codify proper 3-Colouring of the graph G.