Splitting formulas for Tutte polynomials

Artur Andrzejak
Institut für Informatik
Freie Universität Berlin
email: artur@inf.fu-berlin.de
Report B 95-21
December 1995

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Splitting formulas for Tutte polynomials 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 matroid, an extension of the pointed Tutte polynomial introduced by Thomas Brylawski in T.H. Brylawski, A combinatorial model for series-parallel networks, Trans. of the Amer. Math. Soc. 154 (Feb. 1971), 1-22.