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Title: A zero-free interval for chromatic polynomials of nearly 3-connected plane graphs
Authors: Dong, Fengming
Jackson, Bill
Keywords: Planar graph
Potts model partition function
Multivariate Tutte polynomial
Chromatic polynomial
Issue Date: 2011
Citation: Dong, F., & Jackson, B. (2011). A zero-free interval for chromatic polynomials of nearly 3-connected plane graphs. SIAM Journal on Discrete Mathematics, 25(3), 1103-1118.
Abstract: Let G=(V,E) be a nonseparable plane graph on n vertices with at least two edges. Suppose that G has outer face C and that every 2-vertex-cut of G contains at least one vertex of C. Let PG(q) denote the chromatic polynomial of G. We show that (−1)n PG(q)>0 for all 1<q≤1.2040…This result is a corollary of a more general result that (−1)n ZG(q,w)>0 for all 1<q≤1.2040…, where ZG (q,w) is the multivariate Tutte polynomial of G, w={we}e∈E, we =−1 for all e which are not incident to a vertex of C, we ∈ W2 for all e∈E(C), we ∈W1 for all other edges e, and W1, W2 are suitably chosen intervals with −1∈W1 ⊂W2 ⊆(−2,0). -1∈W1⊂W2⊆(-2,0) . Read More:
ISSN: 0895-4801 (online)
Other Identifiers: 10.1137/100790057
Appears in Collections:Journal Articles

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