Finding a dominating set on bipartite graphs
Abstract
Finding a dominating set of minimum cardinality is an NP-hard graph problem, even when the graph is bipartite. In this paper we are interested in solving the problem on graphs having a large independent set. Given a graph $G$ with an independent set of size $z$, we show that the problem can be solved in time $O^*(2^{n-z})$, where $n$ is the number of vertices of $G$. As a consequence, our algorithm is able to solve the dominating set problem on bipartite graphs in time $O^*(2^{n/2})$. Another implication is an algorithm for general graphs whose running time is $O(1.7088^n)$.