Minimizing the Number of Independent Sets in Triangle-Free Regular Graphs

Authors

Jonathan Cutler, Montclair State UniversityFollow
A. J. Radcliffe, University of Nebraska

Document Type

Article

Publication Date

3-1-2018

Journal / Book Title

Discrete Mathematics

Abstract

Recently, Davies, Jenssen, Perkins, and Roberts gave a very nice proof of the result (due, in various parts, to Kahn, Galvin–Tetali, and Zhao) that the independence polynomial of a d-regular graph is maximized by disjoint copies of Kd,d. Their proof uses linear programming bounds on the distribution of a cleverly chosen random variable. In this paper, we use this method to give lower bounds on the independence polynomial of regular graphs. We also give a new bound on the number of independent sets in triangle-free cubic graphs.

DOI

10.1016/j.disc.2017.11.016

MSU Digital Commons Citation

Cutler, Jonathan and Radcliffe, A. J., "Minimizing the Number of Independent Sets in Triangle-Free Regular Graphs" (2018). Department of Mathematics Facuty Scholarship and Creative Works. 105.
https://digitalcommons.montclair.edu/mathsci-facpubs/105

Published Citation

Cutler, J., & Radcliffe, A. J. (2018). Minimizing the number of independent sets in triangle-free regular graphs. Discrete Mathematics, 341(3), 793-800.