Document Type


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Discrete Mathematics


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.



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.

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