Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
Hostname: page-component-77ffc5d9c7-zwn4l Total loading time: 0.287 Render date: 2021-04-23T00:30:27.336Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }
EnglishFrançais
Combinatorics, Probability and Computing Combinatorics, Probability and Computing

Article contents

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)
Corresponding
E-mail address:
jbonin@gwu.edu
omer.gimenez@upc.edu
Get access
Rights & Permissions[Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below.
If you should have access and can't see this content please contact technical support.

References

[1]Björner, A. (1992) The homology and shellability of matroids and geometric lattices. In Matroid Applications (White, N., ed.), Cambridge University Press, pp. 226–283.CrossRefGoogle Scholar
[2]Bonin, J., de Mier, A. and Noy, M. (2003) Lattice path matroids: Enumerative aspects and Tutte polynomials. J. Combin. Theory Ser. A 104 63–94.CrossRefGoogle Scholar
[3]Bonin, J. and de Mier, A. Lattice path matroids: Structural aspects. European J. Combin., to appear.Google Scholar
[4]Brylawski, T. and Oxley, J. G. (1992) The Tutte polynomial and its applications. In Matroid Applications (White, N., ed.), Cambridge University Press, pp. 123–225.CrossRefGoogle Scholar
[5]Colbourn, C. J., Provan, J. S. and Vertigan, D. (1995) The complexity of computing the Tutte polynomial on transversal matroids. Combinatorica 15 1–10.CrossRefGoogle Scholar
[6]Edmonds, J. and Fulkerson, D. R. (1965) Transversals and matroid partition. J. Res. Nat. Bur. Standards Sect. B 69B 147–153.CrossRefGoogle Scholar
[7]Giménez, O. and Noy, M. (2006) On the complexity of computing the Tutte polynomial of bicircular matroids. Combin. Probab. Comput. 15 385–395.CrossRefGoogle Scholar
[8]Jaeger, F., Vertigan, D. and Welsh, D. J. A. (1990) On the computational complexity of the Jones and Tutte polynomials. Math. Proc. Cambridge Philos. Soc. 108 35–53.CrossRefGoogle Scholar
[9]Oxley,, J. G. (1992) Matroid Theory, Oxford University Press.Google Scholar
[10]Vertigan, D. (1998) Bicycle dimension and special points of the Tutte polynomial. J. Combin. Theory Ser. B 74 378–396.CrossRefGoogle Scholar
[11]Vertigan, D. and Welsh, D. J. A. (1992) The computational complexity of the Tutte plane: The bipartite case. Combin. Probab. Comput. 1 181–187.CrossRefGoogle Scholar
[12]Welsh, D. J. A. (1993) Complexity: Knots, Colourings and Counting, Cambridge University Press.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 22 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 23rd April 2021. This data will be updated every 24 hours.

6
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Multi-Path Matroids
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Multi-Path Matroids
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Multi-Path Matroids
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *