Table of Contents
International Journal of Combinatorics
Volume 2012 (2012), Article ID 430859, 40 pages
http://dx.doi.org/10.1155/2012/430859
Review Article

The Tutte Polynomial of Some Matroids

1Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Científica, Circuito Exterior, C.U., Coyoácan, 04510 México City, DF, Mexico
2Escuela de Ciencias, Universidad Autónoma Benito Juárez de Oaxaca, 68120 Oaxaca, OAX, Mexico
3Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana, Azcapozalco, Avenue San Pablo No. 180, Col. Reynosa Tamaulipas, Azcapotzalco, 02200 México City, DF, Mexico

Received 23 February 2012; Accepted 10 July 2012

Academic Editor: Cai Heng Li

Copyright © 2012 Criel Merino et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Tutte polynomial of a graph or a matroid, named after W. T. Tutte, has the important universal property that essentially any multiplicative graph or network invariant with a deletion and contraction reduction must be an evaluation of it. The deletion and contraction operations are natural reductions for many network models arising from a wide range of problems at the heart of computer science, engineering, optimization, physics, and biology. Even though the invariant is #P-hard to compute in general, there are many occasions when we face the task of computing the Tutte polynomial for some families of graphs or matroids. In this work, we compile known formulas for the Tutte polynomial of some families of graphs and matroids. Also, we give brief explanations of the techniques that were used to find the formulas. Hopefully, this will be useful for researchers in Combinatorics and elsewhere.