Find The Largest Forest

Consider two labeled undirected graphs \(G_1(V_1,E)\) and \(G_2(V_2, E)\), each having \(k\) number of edges such that the edge-labels of both graphs are taken from the same set (say \(E=\{1,2,\ldots, k\}\)). The problem is to find the largest collection of edges \(S\subset E\) such that \(S\) is acyclic in both \(G_1\) and \(G_2\).

Which of the following algorithms may be used to solve this problem efficiently?

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