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Comparing Graphs of Different Sizes

Part of: Combinatorial probability Graph theory

Published online by Cambridge University Press:  02 May 2017

RUSSELL LYONS
RUSSELL LYONS*
Affiliation:
Department of Mathematics, Indiana University, 831 East 3rd Street, Bloomington, IN 47405-7106, USA (e-mail: rdlyons@indiana.edu)
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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.

MSC classification

Primary: 05C05: Trees 60C05: Combinatorial probability
Secondary: 05C80: Random graphs 05C81: Random walks on graphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 5 , September 2017 , pp. 681 - 696
Copyright
Copyright © Cambridge University Press 2017 

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