This is a close approximation to the content of my lecture. After a brief survey of well known properties, I present some new interpretations relating to random graphs, lattice point enumeration, and chip firing games. I then examine complexity issues and concentrate in particular, on the existence
Tutte polynomials of q-cones
β Scribed by Joseph E. Bonin; Hongxun Qin
- Book ID
- 108315576
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 96 KB
- Volume
- 232
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
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## 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