### 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 a new bound on the number of independent sets in triangle-free cubic graphs.

Original language | English |
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Pages (from-to) | 793-800 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 341 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2018 |

### Keywords

- Hard-core model
- Independent sets
- Occupancy fraction

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## Cite this

Cutler, J., & Radcliffe, A. J. (2018). Minimizing the number of independent sets in triangle-free regular graphs.

*Discrete Mathematics*,*341*(3), 793-800. https://doi.org/10.1016/j.disc.2017.11.016