Zero-Free Intervals for Flow Polynomials of Near-Cubic Graphs
نویسندگان
چکیده
منابع مشابه
Zero-Free Intervals for Flow Polynomials of Near-Cubic Graphs
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...
متن کاملA 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...
متن کاملOn zero-free intervals of flow polynomials
Article history: Received 10 January 2011 Available online 20 November 2014
متن کاملThe Zero-Free Intervals for Characteristic Polynomials of Matroids
Let M be a loopless matroid with rank r and c components. Let P (M, t) be the characteristic polynomial of M. We shall show that (−1)P (M, t) > (1 − t) for t ∈ (−∞, 1), that the multiplicity of the zeros of P (M, t) at t = 1 is equal to c, and that (−1)r+cP (M, t) > (t− 1) for t ∈ (1, 32 27 ]. Using a result of C. Thomassen we deduce that the maximal zero-free intervals for characteristic polyn...
متن کامل$C_4$-free zero-divisor graphs
In this paper we give a characterization for all commutative rings with $1$ whose zero-divisor graphs are $C_4$-free.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2006
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548306007747