A matroid generalization of a result of Dirac |
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Authors: | James Oxley |
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Institution: | (1) Department of Mathematics, Louisiana State University, 70803-4918 Baton Rouge, Louisiana, USA |
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Abstract: | 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.The author's research was partially supported by a grant from the National Security Agency. |
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Keywords: | 05B35 05C40 |
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