TY - JOUR

T1 - Minimizing the number of independent sets in triangle-free regular graphs

AU - Cutler, Jonathan

AU - Radcliffe, A. J.

PY - 2018/3

Y1 - 2018/3

N2 - 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.

AB - 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.

KW - Hard-core model

KW - Independent sets

KW - Occupancy fraction

UR - http://www.scopus.com/inward/record.url?scp=85038843125&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2017.11.016

DO - 10.1016/j.disc.2017.11.016

M3 - Article

AN - SCOPUS:85038843125

SN - 0012-365X

VL - 341

SP - 793

EP - 800

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 3

ER -