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arXiv · 2111.06026

A Note on the Maximum Number of Minimal Connected Dominating Sets in a Graph

Faisal N. Abu-Khzam
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Abstract

We prove constructively that the maximum possible number of minimal connected dominating sets in a connected undirected graph of order $n$ is in $Ω(1.489^n)$. This improves the previously known lower bound of $Ω(1.4422^n)$ and reduces the gap between lower and upper bounds for input-sensitive enumeration of minimal connected dominating sets in general graphs as well as some special graph classes.

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Faisal N. Abu-Khzam. 2021-11-11. A Note on the Maximum Number of Minimal Connected Dominating Sets in a Graph. https://arxiv.org/abs/2111.06026

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