A Lower Bound on the Average Size of a Connected Vertex Set of a Graph
Combinatorics
2021-03-30 v1
Abstract
The topic is the average order of a connected induced subgraph of a graph. This generalizes, to graphs in general, the average order of a subtree of a tree. In 1984, Jamison proved that the average order, over all trees of order , is minimized by the path . In 2018, Kroeker, Mol, and Oellermann conjectured that minimizes the average order over all connected graphs. The main result of this paper confirms this conjecture.
Cite
@article{arxiv.2103.15174,
title = {A Lower Bound on the Average Size of a Connected Vertex Set of a Graph},
author = {Andrew Vince},
journal= {arXiv preprint arXiv:2103.15174},
year = {2021}
}
Comments
12 pages, 3 figures