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arXiv · 2203.10630

Red Domination in Perfect Elimination Bipartite Graphs

Nesrine Abbas
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Abstract

The $k$ red domination problem for a bipartite graph $G=(X,Y,E)$ is to find a subset $D \subseteq X$ 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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Nesrine Abbas. 2022-03-20. Red Domination in Perfect Elimination Bipartite Graphs. https://arxiv.org/abs/2203.10630

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