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I was making a research about Clique Problem and algorithms. Then I saw that. As this article says, we can find maximal clique in O(n^2) time complexity. Did I misunderstand something or this is a proof that P=NP?

Olivier
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    "Maximal" is different from "the maximum." A maximal clique is simply one that cannot be extended. – גלעד ברקן Oct 21 '21 at 19:58
  • This article describes how to find a random maximal clique for a random vertex in`O(n^2)` where n is the number of vertices in the clique. – RBarryYoung Oct 21 '21 at 20:06
  • @גלעדברקן But doesn't 'clique' mean 'complete graph'? –  Oct 21 '21 at 20:06
  • No, in this case it means “complete sub graph”. As in every vertex in the clique connects to every other one *in the clique*. – RBarryYoung Oct 21 '21 at 20:07
  • @RBarryYoung So 'maximum clique' means 'complete sub-graph with maximum edges' and 'maximal clique' means 'complete sub-graph'. And real 'problem' of clique problem is finding 'maximum clique'. Am I right? –  Oct 21 '21 at 20:13
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    Yes, The article clearly describes the problem that it is solving. It is *not* trying to find the largest clique in the graph. It is finding a random clique that can’t be extended (i.e., “maximal”). – RBarryYoung Oct 21 '21 at 20:18
  • Oh, ok. Thank you for your time. :) –  Oct 21 '21 at 20:22

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