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A generalised exchange theorem for matroid bases

Published online by Cambridge University Press:  17 April 2009

John Donald  and
Malcolm Tobey
John Donald
Affiliation:
Department of Mathematical Sciences, San Diego State University San Diego, CA 92182, United States of America
Malcolm Tobey
Affiliation:
Mathematics Department Southwest, State University Marshall, MN 56258, United States of America
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Abstract

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Let b and c be bases of a matroid. Then for any integer r, there exists an injection σ from r−subsets I of b to r-subsets σ(I) of c such that b – I + σ(I) is a base for all I. This result has implications for the structure of matroid base graphs.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 2 , April 1991 , pp. 177 - 180
Copyright
Copyright © Australian Mathematical Society 1991

References

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