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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

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$71
Individual Members: US$42.60
Institutional Members: US$56.80
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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