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arXiv · 1903.04517

Minimal Dominating Sets in a Tree: Counting, Enumeration, and Extremal Results

Günter Rote
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Abstract

A tree with $n$ vertices has at most $95^{n/13}$ minimal dominating sets. The growth constant $\lambda = \sqrt[13]{95} \approx 1.4194908$ 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.

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Günter Rote. 2019-03-11. Minimal Dominating Sets in a Tree: Counting, Enumeration, and Extremal Results. https://arxiv.org/abs/1903.04517

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