منابع مشابه
An Interpretation for the Tutte Polynomial
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 ow interpretations of T M (1 ? t; 0); T M (0; 1 ? t), Crapo and Rota's nite eld interpretation of T M (1 ? q k ; 0), the interpretation in terms of the Whitney corank-nullity polynom...
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.
متن کاملThe Tutte polynomial
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 of randomized approximation schemes. © 1999 John Wiley & Sons, Inc. Random Struct. Alg., 15, 210–...
متن کاملFourientations and the Tutte polynomial
for α, γ ∈ {0, 1, 2} and β , δ ∈ {0, 1}. We introduce an intersection lattice of 64 cut–cycle fourientation classes enumerated by generalized Tutte polynomial evaluations of this form. We prove these enumerations using a single deletion–contraction argument and classify axiomatically the set of fourientation classes to which our deletion–contraction argument applies. This work unifies and exten...
متن کاملThe multivariate arithmetic Tutte polynomial
We introduce an arithmetic version of the multivariate Tutte polynomial recently studied by Sokal, and a quasi-polynomial that interpolates between the two. We provide a generalized Fortuin-Kasteleyn representation for representable arithmetic matroids, with applications to arithmetic colorings and flows. We give a new proof of the positivity of the coefficients of the arithmetic Tutte polynomi...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1999
ISSN: 0195-6698
DOI: 10.1006/eujc.1998.0275