On circuits and serial symmetric basis-exchange in matroids

Details On circuits and serial symmetric basis-exchange in matroids On circuits and serial symmetric basis-exchange in matroids

2011-10-24

arxiv.org/abs/1110.5166v4

Mathematics

Combinatorics

Scientific paper

The way circuits, relative to a basis, are affected as a result of exchanging a basis element, is studied. As consequences, it is shown that three consecutive symmetric exchanges exist for any two bases of a matroid, and that a full serial symmetric exchange, of length at most 6, exists for any two bases of a matroid of rank 5. A new characterization of binary matroids, related to basis-exchange, is presented.

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