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Is the dominating set problem restricted to planar bipartite graphs of maximum degree 3 NP-complete?

Is maximum independent set NP Hard for Directed Acyclic graphs?

  • I know that we can use Dilworth's theorem to solve it If the DAG represented a partially ordered set, But what about general DAGs

  • Answer:

    My current argument is Yes, it's NP Hard. Why ? since we can always convert an undirected graph to a DAG by putting directions on the edges, a simple method is to assign directions of edges such that they go from higher numbered nodes to lower numbered ones. for example if u > v, and there's an edge between u and v then make this edge direction go from u to v. Now as we converted the undirected graph to a DAG if we had an algorithm that solves maximum independent set for a general DAG we could solve it for general undirected graphs.

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