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Multi-Path Matroids

Published online by Cambridge University Press:  01 March 2007

Department of Mathematics, The George Washington University, Washington, DC 20052, USA (e-mail:
Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1–3, 08034, Barcelona, Spaine (e-mail:


We introduce the minor-closed, dual-closed class of multi-path matroids. We give a polynomial-time algorithm for computing the Tutte polynomial of a multi-path matroid, we describe their basis activities, and we prove some basic structural properties. Key elements of this work are two complementary perspectives we develop for these matroids: on the one hand, multi-path matroids are transversal matroids that have special types of presentations; on the other hand, the bases of multi-path matroids can be viewed as sets of lattice paths in certain planar diagrams.

Copyright © Cambridge University Press 2006

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