We prove constructively that the maximum possible number of minimal connected dominating sets in a connected undirected graph of order $n$ is in $\Omega(1.489^n)$. This improves the previously known lower bound of $\Omega(1.4422^n)$ 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.
翻译:我们建设性地证明,在一个链接的无方向的顺序图中,最起码的连接占支配地位的组数以美元表示(1.489美元),这改进了以前已知的较低约束值(1.44222美元),并缩小了一般图表中输入敏感度最小连接占支配地位组数以及某些特殊图表类别中输入敏感度组数的下限和上限值之间的差距。