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clique_removal

clique_removal(G)

Repeatedly remove cliques from the graph.

Results in a \(O(|V|/(\log |V|)^2)\) approximation of maximum clique & independent set. Returns the largest independent set found, along with found maximal cliques.

Parameters:

G : NetworkX graph

Undirected graph

Returns:

max_ind_cliques : (set, list) tuple

Maximal independent set and list of maximal cliques (sets) in the graph.

References

[R141]

Boppana, R., & Halldórsson, M. M. (1992). Approximating maximum independent sets by excluding subgraphs. BIT Numerical Mathematics, 32(2), 180–196. Springer.