I have a set of investors (say n), and a set of startups (say m). At the start, I have all the investors say either yes or no to the startup (which corresponds to whether they want to interact with them or not).
Now, I have to conduct a networking event of r rounds considering this scenario. In each round, I match investors with startups they want to meet (one investor with one startup). I want to conduct the rounds such that the sum of the startups they met, across all investors, is maximum.
Now, if r=1, this reduces to the maximum bipartite matching problem. Does anyone have any ideas on how to solve this for r>1? I have been thinking along the lines of having the source and sink edge capacities to be r instead of 1, but I am unable to prove that this works.