Efficient Enumeration of Dominating Sets for Sparse Graphs

Dominating sets are fundamental graph structures. However, enumeration of dominating sets has not received much attention. This study aims to propose two efficient enumeration algorithms for sparse graphs. The first algorithm enumerates all the dominating sets for k-degenerate graphs in O (k) time per solution using O (n + m) space. Since planar graphs have a constant degeneracy, this algorithm can enumerate all such sets for planar graphs in constant time per solution. The other algorithm enumerates all the dominating sets in constant time per solution for input graphs with a girth of at least nine.