The maximum number of minimal dominating sets in a tree
Günter Rote · Symposium on Discrete Algorithms · 2019
A tree with n vertices has at most 95n/13 minimal dominating sets. The growth constant [MATH HERE] is best possible. It is obtained in a semi-automatic way as a kind of dominant eigenvalue of a bilinear operation on sixtuples that is derived from the dynamic-programming recursion for computing the number of minimal dominating sets of a tree. We also derive an output-sensitive algorithm for listing all minimal dominating sets with linear set-up time and linear delay between successive solutions.