Comparing Graphs of Different Sizes
Combinatorics
2018-09-10 v2 Probability
Abstract
We consider two notions describing how one finite graph may be larger than another. Using them, we prove several theorems for such pairs that compare the number of spanning trees, the return probabilities of random walks, and the number of independent sets, among other combinatorial quantities. Our methods involve inequalities for determinants, for traces of functions of operators, and for entropy.
Cite
@article{arxiv.1602.06995,
title = {Comparing Graphs of Different Sizes},
author = {Russell Lyons},
journal= {arXiv preprint arXiv:1602.06995},
year = {2018}
}
Comments
17 pages, 6 figures