Minimum possible Clique in a Graph

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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)
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