MINIMIZING THE NUMBER OF INDEPENDENT SETS IN TRIANGLE-FREE REGULAR GRAPHS

Authors

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

Date of this Version

2016

Citation

Volume 341, Issue 3, March 2018, Pages 793-800

Comments

Published in Discrete Mathematics

https://doi.org/10.1016/j.disc.2017.11.016

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 K_d,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 new bounds on the number of independent sets in triangle-free regular graphs.