For claw-free graphs, the independence polynomial is proven zero-free in a disk of radius at least 1/(2Delta+1), beating Shearer's radius for degree at least 4, and a new signed forest-sum identity for the polynomial is established.
Barvinok, Combinatorics and Complexity of Partition Functions , Algorithms and Com- binatorics 30, Springer (2016)
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On the independent set polynomial of graphs and claw-free graphs
For claw-free graphs, the independence polynomial is proven zero-free in a disk of radius at least 1/(2Delta+1), beating Shearer's radius for degree at least 4, and a new signed forest-sum identity for the polynomial is established.