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