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On Minimally 3-Connected Binary Matroids

Published online by Cambridge University Press:  10 December 2001

TALMAGE JAMES REID  and
HAIDONG WU
TALMAGE JAMES REID
Affiliation:
Department of Mathematics, The University of Mississippi, University, MS 38677, USA; (e-mail: mmreid@olemiss.edu)
HAIDONG WU
Affiliation:
Department of Mathematics, Southern University, Baton Rouge, Louisiana, LA 70813, USA; (e-mail: hwu@olemiss.edu)
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Abstract

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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}.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 10 , Issue 5 , September 2001 , pp. 453 - 461
Copyright
2001 Cambridge University Press