A zero-free interval for flow polynomials of cubic graphs
نویسندگان
چکیده
منابع مشابه
A zero-free interval for flow polynomials of cubic graphs
Let P(G, t) and F(G, t) denote the chromatic and flow polynomials of a graph G. D.R. Woodall has shown that, if G is a plane triangulation, then the only zeros of P(G, t) in (−∞,γ) are 0, 1 and 2, where γ ≈ 2.54 . . . is the zero in (2,3) of the chromatic polynomial of the octahedron. The main purpose of this paper is to remove the planarity hypothesis from Woodall’s theorem by showing that the...
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Let P(G, t) and F(G, t) denote the chromatic and flow polynomials of a graph G. G.D. Birkhoff and D.C. Lewis showed that, if G is a plane near triangulation, then the only zeros of P(G, t) in (−∞,2] are 0, 1 and 2. We will extend their theorem by showing that a stonger result to the dual statement holds for both planar and non-planar graphs: if G is a bridgeless graph with at most one vertex of...
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Woodall, D.R., A zero-free interval for chromatic polynomials, Discrete Mathematics 101 (1992) 333-341. It is proved that, for a wide class of near-triangulations of the plane, the chromatic polynomial has no zeros between 2 and 2.5. Together with a previously known result, this shows that the zero of the chromatic polynomial of the octahedron at 2.546602. . . is the smallest non-integer real z...
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Let G = (V,E) be a 2-connected plane graph on n vertices with outer face C such 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)nPG(q) > 0 for all 1 < q ≤ 1.2040.... This result is a corollary of a more general result that (−1)ZG(q,w) > 0 for all 1 < q ≤ 1.2040..., where ZG(q,w) is the multivariate Tutte polynomial...
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Article history: Received 10 January 2011 Available online 20 November 2014
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2007
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2006.04.006