Abstract
This work concentrates on finding maximum clique from undirected and unweighted graphs. Maximum clique problem is one of the most known NP-complete problems, the most complex problems of NP class. A lot of other problems can be transformed into clique problem, therefore solving or at least finding a faster algorithm for finding clique will automatically help to solve lots of other tasks. The main contribution of this work is a new exact algorithm for finding maximum clique, which works faster than any currently existing algorithm on a wide variety of graphs. The main idea is to combine a number of efficient improvements from different algorithms into a new one. At first sight these improvements cannot cooperate together, but a new approach of skipping vertices from further expanding instead of pruning the whole branch allows to use all the upgrades at ones. There will be some step-by-step examples with explanations which demonstrate how to use a proposed algorithm.
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