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I have an arbitrary directed, non-complete graph. I would like to find a maximal subset of nodes within that graph such that the induced subgraph has no cycles. I'm sure there must be a name for this problem in the literature - do you know what it is?

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  • $\begingroup$ Thanks! Do you know how I can mark the question as answered, given that you answered in a comment? $\endgroup$ – lightning Dec 2 '18 at 3:51
  • $\begingroup$ I just transferred my comment to answer. So I will delete that comment. $\endgroup$ – Michael Dec 2 '18 at 4:55
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This is the "maximum acyclic subgraph" problem (just search Google).

I once used such a thing for an info-theory bound on an "index coding" problem (but for a directed graph in that case), Lemma 1 here:

http://ee.usc.edu/stochastic-nets/docs/dynamic-index-coding-it.pdf

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