منابع مشابه
Some inequalities for the Tutte polynomial
We prove that the Tutte polynomial of a coloopless paving matroid is convex along the portions of the line segments x + y = p lying in the positive quadrant. Every coloopless paving matroid is in the class of matroids which contain two disjoint bases or whose ground set is the union of two bases. For this latter class we give a proof that TM (a, a) ≤ max{TM (2a, 0), TM (0, 2a)} for a ≥ 2. We co...
متن کاملextensions of some polynomial inequalities to the polar derivative
توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولA note on some inequalities for the Tutte polynomial of a matroid
We prove that if a matroid M contains two disjoint bases (or, dually, if its ground set is the union of two bases), then TM (a, a) ≤ max{TM (2a, 0), TM (0, 2a)} for a ≥ 2. This resembles the conjecture that appears in C. Merino and D.J.A. Welsh, Forests, colourings and acyclic orientations of the square lattice, Annals of Combinatorics 3 (1999) pp. 417–429: If G is a 2-connected graph with no l...
متن کاملSome new evaluations of the Tutte polynomial
Interpretations for evaluations of the Tutte polynomial T (G;x, y) of a graph G are given at a number of points on the hyperbolae Hq = {(x, y) | (x − 1)(y − 1) = q}, for q a positive integer — points at which there are usually no other similarly meaningful graphical interpretations. Further, when q is a prime power, an alternative interpretation for the evaluation of the Tutte polynomial at (1−...
متن کاملOn the tutte polynomial of benzenoid chains
The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2011
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2010.11.005