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Multi-Path Matroids

Published online by Cambridge University Press:  01 March 2007

JOSEPH E. BONIN  and
OMER GIMÉNEZ
JOSEPH E. BONIN
Affiliation:
Department of Mathematics, The George Washington University, Washington, DC 20052, USA (e-mail: jbonin@gwu.edu)
OMER GIMÉNEZ
Affiliation:
Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1–3, 08034, Barcelona, Spaine (e-mail: omer.gimenez@upc.edu)
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Abstract

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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 2 , March 2007 , pp. 193 - 217
Copyright
Copyright © Cambridge University Press 2006

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