Tutte Polynomials of Generalized Parallel Connections

Parametrized Tutte Polynomials of Graphs and Matroids

We generalize and unify results on parametrized and coloured Tutte polynomials of graphs and matroids due to Zaslavsky, and Bollobás and Riordan. We give a generalized Zaslavsky– Bollobás–Riordan theorem that characterizes parametrized contraction–deletion functions on minor-closed classes of matroids, as well as the modifications necessary to apply the discussion to classes of graphs. In gener...

Parallel connections and coloured Tutte polynomials

We give formulas for the Tutte polynomials of parallel and series connections of weightedmatroids, generalizing and unifying formulas of Oxley and Welsh (Discrete Math. 109 (1992) 185), Bollobás and Riordan (Comb. Probab. Comput. 8 (1999) 45) and Woodall (Discrete Math. 247 (2002) 201). © 2004 Elsevier B.V. All rights reserved.

Tutte Polynomials of Flower Graphs

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.

Splitting Formulas for Tutte Polynomials

We present two splitting formulas for calculating the Tutte polynomial of a matroid. The rst 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 matroid, an extension of the pointed Tutte polynomial introduced by Thomas Brylawski in Bry71].