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Find the minimum possible size of a clique in a graph, that can be formed using n nodes and e edges. The component should be a complete graph.

In other words, Find min size of subset of vertices such that every two distinct vertices that has a unique edge between all it's nodes.

  • The given graph is considered to be undirected.
  • Size refers to number of nodes in the clique.

example:

  • given 5 nodes and 6 edges, min size of complete graph is 2 (visualization)
  • given 5 nodes and 7 edges, min size of complete graph is 3 (visualization)
trovi
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    Cool question! Would you mind sharing your attempts at this problem? – Marat Sep 16 '21 at 15:06
  • The word "component" is very confusing here because your problem is completely unrelated to "connected components". I think what you mean is "nodes-induced subgraph". – Stef Sep 16 '21 at 15:09
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    @Stef If I understand the question right, it's about min [clique](https://en.wikipedia.org/wiki/Clique_(graph_theory)) size – Marat Sep 16 '21 at 15:27
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    [this question](https://math.stackexchange.com/questions/1279241/minimum-size-of-largest-clique-in-a-graph) might be helpful – Marat Sep 16 '21 at 15:29
  • @Marat, you are right the question is about clique, I will go ahead and update the question to incorporate that – trovi Sep 17 '21 at 02:11
  • @Marat the link of the question you shared was what I was looking for, I will go ahead and post that answer here too, so that it helps in future. – trovi Sep 17 '21 at 02:18

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