# On the zeroes of hypergraph independence polynomials

@article{Galvin2022OnTZ, title={On the zeroes of hypergraph independence polynomials}, author={David J. Galvin and Gweneth McKinley and Will Perkins and Michail Sarantis and Prasad Tetali}, journal={ArXiv}, year={2022}, volume={abs/2211.00464} }

We study the locations of complex zeroes of independence polynomials of bounded degree hypergraphs. For graphs, this is a long-studied subject with applications to statistical physics, algorithms, and combinatorics. Results on zero-free regions for bounded-degree graphs include Shearer’s result on the optimal zero-free disk, along with several recent results on other zero-free regions. Much less is known for hypergraphs. We make some steps towards an understanding of zero-free regions for…

## References

SHOWING 1-10 OF 64 REFERENCES

### The limit of the zero locus of the independence polynomial for bounded degree graphs

- Mathematics
- 2021

The goal of this paper is to accurately describe the maximal zero-free region of the independence polynomial for graphs of bounded degree, for large degree bounds. In previous work with de Boer,…

### Computing the Independence Polynomial: from the Tree Threshold down to the Roots

- Mathematics, Computer ScienceSODA
- 2018

An algorithm for approximating the multivariate independence polynomial Z(z), with negative and complex arguments, with novel multivariate form of the correlation decay technique, which can handle non-uniform complex parameters and gives a deterministic algorithm for Shearer's lemma.

### Zero-Free Regions of Partition Functions with Applications to Algorithms and Graph Limits

- Mathematics, Computer ScienceComb.
- 2018

A class of edge-coloring models whose partition functions do not evaluate to zero on bounded degree graphs is identified and a quasi-polynomial time approximation scheme for computing these partition functions is given.

### On complex roots of the independence polynomial

- MathematicsArXiv
- 2022

. It is known from the work of Shearer [15] (see also Scott and Sokal [14]) that the independence polynomial 𝑍 𝐺 ( 𝜆 ) of a graph 𝐺 of maximum degree at most 𝑑 + 1 does not vanish provided that…

### Inapproximability of the independent set polynomial in the complex plane

- MathematicsSTOC
- 2018

The main result shows that for every λ outside of ΛΔ, the problem of approximating ZG(λ) on graphs G with maximum degree at most Δ is indeed NP-hard, and on the negative real axis, it is #P-hard to even decide whether ZG (λ)>0, resolving in the affirmative a conjecture of Harvey, Srivastava and Vondrak.

### Homomorphisms from the torus

- Mathematics
- 2020

We present a detailed probabilistic and structural analysis of the set of weighted homomorphisms from the discrete torus $\mathbb{Z}_m^n$, where $m$ is even, to any fixed graph: we show that the…

### Computing the partition function for graph homomorphisms with multiplicities

- Mathematics, Computer ScienceJ. Comb. Theory, Ser. A
- 2016

### On a conjecture of Sokal concerning roots of the independence polynomial

- MathematicsMichigan Mathematical Journal
- 2019

It is shown that Sokal's Conjecture holds, as well as a multivariate version, and optimality for the domain of non-vanishing for independence polynomials of graphs is proved.

### The Probability of Non-Existence of a Subgraph in a Moderately Sparse Random Graph

- MathematicsCombinatorics, Probability and Computing
- 2018

A general procedure that finds recursions for statistics counting isomorphic copies of a graph G0 in the common random graph models and gives much information on the distribution of the number of copies of G0 that are not in large ‘clusters’ of copies is developed.