For any matroid M realizable over Q , we give a combinatorial interpretation of the Tutte polynomial T M (x, y) which generalizes many of its known interpretations and specializations, including Tutte's coloring and flow interpretations of T M (1t, 0), T M (0, 1t); Crapo and Rota's finite field inte
An inequality for Tutte polynomials
β Scribed by Bill Jackson
- Publisher
- Springer-Verlag
- Year
- 2010
- Tongue
- English
- Weight
- 447 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Woodall, D.R., An inequality for chromatic polynomials, Discrete Mathematics 101 (1992) 327-331. It is proved that if P(G, t) is the chromatic polynomial of a simple graph G with II vertices, m edges, c components and b blocks, and if t S 1, then IP(G, t)/ 2 1t'(tl)hl(l + ys + ys2+ . + yF' +spl), wh
## Abstract We define two twoβvariable polynomials for rooted trees and one twoβvariable polynomial for unrooted trees, all of which are based on the coranknullity formulation of the Tutte polynomial of a graph or matroid. For the rooted polynomials, we show that the polynomial completely determine
We present two splitting formulas for calculating the Tutte polynomial of a matroid. The first one is for a generalized parallel connection across a 3-point line of two matroids and the second one is applicable to a 3-sum of two matroids. An important tool used is the bipointed Tutte polynomial of a