The Tutte polynomial
نویسنده
چکیده
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, 210–228, 1999
منابع مشابه
Tutte polynomials of wheels via generating functions
We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.
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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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Suppose G is an nvertex and medge simple graph with edge set E(G). An integervalued function f: E(G) → Z is called a flow. Tutte was introduced the flow polynomial F(G, λ) as a polynomial in an indeterminate λ with integer coefficients by F(G,λ) In this paper the Flow polynomial of some dendrimers are computed.
متن کاملRelative Tutte Polynomials for Coloured Graphs and Virtual Knot Theory
We introduce the concept of a relative Tutte polynomial. We show that the relative Tutte polynomial can be computed in a way similar to the classical spanning tree expansion used by Tutte in his original paper on this subject. We then apply the relative Tutte polynomial to virtual knot theory. More specifically, we show that the Kauffman bracket polynomial (hence the Jones polynomial) of a virt...
متن کاملOn the Homfly and Tutte Polynomials
A celebrated result of F. Jaeger states that the Tutte polynomial of a planar graph is determined by the HOMFLY polynomial of an associated link. Here we are interested in the converse of this result. We consider the question ‘to what extent does the Tutte polynomial determine the HOMFLY polynomial of any knot?’ We show that the HOMFLY polynomial of a knot is determined by Tutte polynomials of ...
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ورودعنوان ژورنال:
- Random Struct. Algorithms
دوره 15 شماره
صفحات -
تاریخ انتشار 1999