2025-06-27
Optimal zero-free regions for the independence polynomial of bounded degree hypergraphs
Publication
Publication
Random Structures & Algorithms , Volume 66 - Issue 4 p. e70018:1- e70018:32
In this paper, we investigate the distribution of zeros of the independence polynomial of hypergraphs of maximum degree (Formula presented.). For graphs, the largest zero-free disk around zero was described by Shearer as having radius (Formula presented.). Recently, it was shown by Galvin et al. that for hypergraphs the disk of radius (Formula presented.) is zero-free; however, it was conjectured that the actual truth should be (Formula presented.). We show that this is indeed the case. We also show that there exists an open region around the interval (Formula presented.) that is zero-free for hypergraphs of maximum degree (Formula presented.), which extends the result of Peters and Regts from graphs to hypergraphs. Finally, we determine the radius of the largest zero-free disk for the family of bounded degree (Formula presented.) -uniform linear hypertrees in terms of (Formula presented.) and (Formula presented.).
| Additional Metadata | |
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| , , | |
| doi.org/10.1002/rsa.70018 | |
| Random Structures & Algorithms | |
| Partition functions of large-degree networks | |
| Organisation | Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands |
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Bencs, F., & Buys, P. (2025). Optimal zero-free regions for the independence polynomial of bounded degree hypergraphs. Random Structures & Algorithms, 66(4), e70018:1–e70018:32. doi:10.1002/rsa.70018 |
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