๐”– Bobbio Scriptorium
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The Tutte polynomial

โœ Scribed by Dominic Welsh


Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
151 KB
Volume
15
Category
Article
ISSN
1042-9832

No coin nor oath required. For personal study only.

โœฆ Synopsis


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.


๐Ÿ“œ SIMILAR VOLUMES


An Interpretation for the Tutte Polynomi
โœ V Reiner ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 204 KB

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

A Convolution Formula for the Tutte Poly
โœ W. Kook; V. Reiner; D. Stanton ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 75 KB

Following Crapo [2], let `(x, y)(M)=x r(M) y r(M\*) , where K=Z[x, y]. Lemma 1. `(x, y) &1 =`(&x, &y).

Splitting Formulas for Tutte Polynomials
โœ Artur Andrzejak ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 371 KB

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

The Coefficients of the Tutte Polynomial
โœ W. Schwarzler ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 102 KB

W. T. Tutte conjectured that the coefficients \(t_{i, j}\) of his dichromate form unimodal sequences in \(i\) and \(j\) separately. P. D. Seymour and D. J. A. Welsh conjectured more generally that the same holds for the coefficients of the Tutte polynomial of an arbitrary matroid. We show, by an exa

Bicycle Dimension and Special Points of
โœ Dirk Vertigan ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 308 KB

For each pair of algebraic numbers (x, y) and each field F, the complexity of computing the Tutte polynomial T(M; x, y) of a matroid M representable over F is determined. This computation is found to be \*P-complete except when (x&1)( y&1)=1 or when |F| divides (x&1)( y&1) and (x, y) is one of the s