Jump to ContentJump to Main Navigation
Matroid Theory$
Users without a subscription are not able to see the full content.

James Oxley

Print publication date: 2011

Print ISBN-13: 9780198566946

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780198566946.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 24 July 2019

The Splitter Theorem

The Splitter Theorem

Chapter:
(p.457) 12 The Splitter Theorem
Source:
Matroid Theory
Author(s):

James Oxley

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566946.003.0013

This chapter states and proves Seymour's Splitter Theorem. This result, which is a generalization of Tutte's Wheels-and-Whirls Theorem (8.8.4), is a very powerful general tool for deriving matroid structure results. The Wheels-and-Whirls Theorem determines when we can find some element in a 3-connected matroid M to delete or contract in order to preserve 3-connectedness. The Splitter Theorem considers when such an element removal is possible that will not only preserve 3-connectedness but will also maintain the presence of an isomorphic copy of some specified minor of M. The chapter illustrates the power of the Splitter Theorem by noting a variety of consequences of it. It also discusses some extensions and generalizations of the theorem.

Keywords:   matroids, Tutte's Wheels-and-Whirls Theorem, 3-connectedness

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .