A matroid generalization of a result of Dirac


This paper generalizes a theorem of Dirac for graphs by proving that ifM is a 3-connected matroid, then, for all pairs {a,b} of distinct elements ofM and all cocircuitsC * ofM, there is a circuit that contains {a,b} and meetsC *. It is also shown that, although the converse of this result fails, the specified condition can be used to characterize 3-connected matroids.

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The author's research was partially supported by a grant from the National Security Agency.

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Oxley, J. A matroid generalization of a result of Dirac. Combinatorica 17, 267–273 (1997). https://doi.org/10.1007/BF01200909

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Mathematics Subject Classification (1991)

  • 05B35
  • 05C40