A zero-free interval for chromatic polynomials
نویسنده
چکیده
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 zero of any chromatic polynomial of a plane triangulation.
منابع مشابه
On upper bounds for real roots of chromatic polynomials
For any positive integer n, let Gn denote the set of simple graphs of order n. For any graph G in Gn, let P(G; ) denote its chromatic polynomial. In this paper, we -rst show that if G ∈Gn and (G)6 n− 3, then P(G; ) is zero-free in the interval (n − 4 + =6 − 2= ;+∞), where = (108 + 12√93)1=3 and =6 − 2= (=0:682327804 : : :) is the only real root of x + x − 1; we proceed to prove that whenever n ...
متن کاملChromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs
In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...
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 کاملChromatic polynomials of some nanostars
Let G be a simple graph and (G,) denotes the number of proper vertex colourings of G with at most colours, which is for a fixed graph G , a polynomial in , which is called the chromatic polynomial of G . Using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some nanostars.
متن کاملThe largest real zero of the chromatic polynomial
It is proved that if every subcontraction of a graph G contains a vertex with degree at most k, then the chromatic polynomial of G is positive throughout the interval (k, c~); Kk+l shows that this interval is the largest possible. It is conjectured that the largest real zero of the chromatic polynomial of a z-chromatic planar graph is always less than X. For Z = 2 and 3, constructions are given...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 101 شماره
صفحات -
تاریخ انتشار 1992