Efficient Enumeration Algorithm for Dominating Sets in Bounded Degenerate Graphs (Foundations and Applications of Algorithms and Computation)

Abstract

Dominating sets are fundamental graph structures. However, enumeration of dominating sets has not received much attention. This study aims to propose an efficient enumeration algorithms for bounded degenerate graphs. The 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.