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The Internally 4-Connected Binary Matroids with No $M(K_{3,3})$-Minor

Dillon Mayhew Victoria University of Wellington, Wellington, New Zealand
Gordon Royle University of Western Australia, Crawley, Western Australia
Geoff Whittle Victoria University of Wellington, Wellington, New Zealand
Available Formats:
Electronic ISBN: 978-1-4704-0595-3
Product Code: MEMO/208/981.E
List Price: $71.00 MAA Member Price:$63.90
AMS Member Price: $42.60 Click above image for expanded view The Internally 4-Connected Binary Matroids with No$M(K_{3,3})$-Minor Dillon Mayhew Victoria University of Wellington, Wellington, New Zealand Gordon Royle University of Western Australia, Crawley, Western Australia Geoff Whittle Victoria University of Wellington, Wellington, New Zealand Available Formats:  Electronic ISBN: 978-1-4704-0595-3 Product Code: MEMO/208/981.E  List Price:$71.00 MAA Member Price: $63.90 AMS Member Price:$42.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 2082010; 95 pp
MSC: Primary 05;

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.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Möbius matroids
• 4. From internal to vertical connectivity
• 5. An $R_{12}$-type matroid
• 6. A connectivity lemma
• 7. Proof of the main result
• A. Case-checking
• C. Allowable triangles
• Requests

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Volume: 2082010; 95 pp
MSC: Primary 05;

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.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Möbius matroids
• 4. From internal to vertical connectivity
• 5. An $R_{12}$-type matroid
• 6. A connectivity lemma
• 7. Proof of the main result
• A. Case-checking