On the Number of Connected Sets in Bounded Degree Graphs
On the Number of Connected Sets in Bounded Degree Graphs
A set of vertices in a graph is connected if it induces a connected subgraph. Using Shearer's entropy lemma and a computer search, we show that the number of connected sets in a graph with $n$ vertices and maximum vertex degree $d$ is at most $O(1.9351^n)$ for $d=3$, $O(1.9812^n)$ for …