Red Domination in Perfect Elimination Bipartite Graphs
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The k red domination problem for a bipartite graph G=(X,Y,E) is to find a subset D ⊆ X of cardinality at most k that dominates vertices of Y. The decision version of this problem is NP-complete for general bipartite graphs but solvable in polynomial time for chordal bipartite graphs. We strengthen that result by showing that it is NP-complete for perfect elimination bipartite graphs. We present a tight upper bound on the number of such sets in bipartite graphs, and show that we can calculate that number in linear time for convex bipartite graphs. We present a linear space linear delay enumeration algorithm that needs only linear preprocessing time.
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