New methods to color the vertices of a graph
Communications of the ACM
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Computers and Intractability; A Guide to the Theory of NP-Completeness
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Computer Vision
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
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An efficient branch-and-bound algorithm for finding a maximum clique
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
An algorithm for finding a maximum clique in a graph
Operations Research Letters
On places suitable for applying AI principles in NP-hard graph problems' algorithms
AIAP'07 Proceedings of the 25th conference on Proceedings of the 25th IASTED International Multi-Conference: artificial intelligence and applications
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In this paper two best known at the moment algorithms for finding the maximum clique is compared. A key technique that both algorithms rely on is using a heuristic vertex colouring. The only difference between those algorithms is a way of using vertex-colouring and this difference in the very important. The algorithms' approaches are divided in this paper into two classes: re-applying vertex colouring on each depth and re-using colour classes obtained before the start of the main part. Historical attempts to use the colour classes for the maximum clique finding are also reviewed. Those two algorithms were never compared so far as is not widely announced also. The comparison is essential information for finding further development ways.