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The Internally 4-Connected Binary Matroids with No \(M(K_{3,3})\)-Minor
Dillon Mayhew, Victoria University of Wellington, New Zealand, Gordon Royle, University of Western Australia, Crawley, Western Australia, and Geoff Whittle, Victoria University of Wellington, New Zealand
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Memoirs of the American Mathematical Society
2010; 95 pp; softcover
Volume: 208
ISBN-10: 0-8218-4826-7
ISBN-13: 978-0-8218-4826-5
List Price: US$67
Individual Members: US$40.20
Institutional Members: US$53.60
Order Code: MEMO/208/981
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The authors give a characterization of the internally \(4\)-connected binary matroids that have no minor isomorphic to \(M(K_{3,3})\). Any such matroid is either cographic, or is isomorphic to a particular single-element extension of the bond matroid of a cubic or quartic Möbius ladder, or is isomorphic to one of eighteen sporadic matroids.

Table of Contents

  • Introduction
  • Preliminaries
  • Möbius matroids
  • From internal to vertical connectivity
  • An \(R_{12}\)-type matroid
  • A connectivity lemma
  • Proof of the main result
  • Appendix A. Case-checking
  • Appendix B. Sporadic matroids
  • Appendix C. Allowable triangles
  • Bibliography
  • Index
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