Question: 1. Suppose you have a network G = (V, E), not necessarily bipartite. Consider the following random algorithm for obtaining a matching: Let M =

1. Suppose you have a network G = (V, E), not necessarily bipartite. Consider the following random algorithm for obtaining a matching:

Let M = .

While there exists an edge e such that M e is a matching: Add e to M.

Return M.

In other words, keep adding edges arbitrarily until you cant add any more. Prove that when this algorithm terminates, the size of M is at least half the size of the maximum matching.

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