The path minimises the average size of a connected induced subgraph
Combinatorics
2024-02-06 v4
Abstract
We prove that among all graphs of order n, the path uniquely minimises the average order of its connected induced subgraphs. This confirms a conjecture of Kroeker, Mol and Oellermann, and generalises a classical result of Jamison for trees, as well as giving a new, shorter proof of the latter. While this paper was being prepared, a different proof was given by Andrew Vince.
Cite
@article{arxiv.2103.16491,
title = {The path minimises the average size of a connected induced subgraph},
author = {John Haslegrave},
journal= {arXiv preprint arXiv:2103.16491},
year = {2024}
}
Comments
9 pages, 1 figure. Fixed a few typos