Circuits and Cocircuits in Regular Matroids |
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Authors: | Dillon Mayhew |
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Affiliation: | (1) Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford, OX1 3LB, UK;(2) Present address: School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, P.O. BOX 600, Wellington, New Zealand |
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Abstract: | A classical result of Dirac's shows that, for any two edges and any n−2 vertices in a simple n-connected graph, there is a cycle that contains both edges and all n−2 of the vertices. Oxley has asked whether, for any two elements and any n−2 cocircuits in an n-connected matroid, there is a circuit that contains both elements and that has a non-empty intersection with all n−2 of the cocircuits. By using Seymour's decomposition theorem and results of Oxley and Denley and Wu, we prove that a slightly stronger property holds for regular matroids. |
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Keywords: | Dirac Regular matroids Circuits Cocircuits |
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