On Minimally 3-Connected Binary Matroids

We generalize a minimal 3-connectivity result of Halin from graphs to binary matroids. As applications of this theorem to minimally 3-connected matroids, we obtain new results and short inductive proofs of results of Oxley and Wu. We also give new short inductive proofs of results of Dirac and Halin...

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Bibliographic Details
Published inCombinatorics, probability & computing Vol. 10; no. 5; pp. 453 - 461
Main Authors REID, TALMAGE JAMES, WU, HAIDONG
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.09.2001
Subjects
Combinatorial analysis
Computation
Graphs
Proving
Theorems
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Summary:We generalize a minimal 3-connectivity result of Halin from graphs to binary matroids. As applications of this theorem to minimally 3-connected matroids, we obtain new results and short inductive proofs of results of Oxley and Wu. We also give new short inductive proofs of results of Dirac and Halin on minimally k-connected graphs for k ∈ {2,3}.
Bibliography:PII:S0963548301004850
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ISSN:0963-5483
1469-2163
DOI:10.1017/S0963548301004850