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A question about the clique problem (specifically k-clique). Is there any algorithm that takes advantage of the properties of connected graphs to find cliques of a given size k, if such cliques exist?

Paul Manta
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  • do you mean graphs with disconnected subgraphs? (I don't know the exact terminology, apologies if that doesn't make sense). – didierc Dec 14 '12 at 00:30
  • you can't have a graph without connected components, unless the graph has no verts. – goat Dec 14 '12 at 00:45
  • @didierc Yes, I think that's it. I'm not very familiar with the terminology either. I guess I'll just change the question to say "islands". – Paul Manta Dec 14 '12 at 00:54
  • @tmyklebu It seems the term I was looking for is "connected graphs". – Paul Manta Dec 14 '12 at 06:28

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Any algorithm can be made to take advantage of connected components. Just find the connected components before running the algorithm, discard those smaller than k and run the algorithm separately on each of the remaining ones.

Rafał Dowgird
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