Based on a technique of Barvinok [4,5,6] and Barvinok and Soberón [8,9] we identify a class of edge-coloring models whose partition functions do not evaluate to zero on bounded degree graphs. Subsequently we give a quasi-polynomial time approximation scheme for computing these partition functions. As another application we show that the normalised partition functions of these models are continuous with respect to the Benjamini-Schramm topology on bounded degree graphs. We moreover give quasi-polynomial time approxi-mation schemes for evaluating a large class of graph polynomials, including the Tutte polynomial, on bounded degree graphs.
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Regts, G. Zero-Free Regions of Partition Functions with Applications to Algorithms and Graph Limits. Combinatorica 38, 987–1015 (2018). https://doi.org/10.1007/s00493-016-3506-7
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