2016/11/02 by Lokshtanov, Daniel, Pilipczuk, Michał, Saurabh, Saket
#Combinatorics (math.CO) #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.1611.00840
A vertex subset S in a graph G is a dominating set if every vertex not contained in S has a neighbor in S. A dominating set S is a connected dominating set if the subgraph G[S] induced by S is connected. A connected dominating set S is a minimal connected dominating set if no proper subset of S is also a connected dominating set. We prove that there exists a constant ε > 10-50 such that every graph G on n vertices has at most O(2(1-ε)n) minimal connected dominating sets. For the same ε we also give an algorithm with running time 2(1-ε)n⋅ nO(1) to enumerate all minimal connected dominating sets in an input graph G.