Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-23T19:34:27.537Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Brualdi, R.A., ‘Comments on bases in dependence structures’, Bull. Austral. Math. Soc. 1 (1969), 161–167.CrossRefGoogle Scholar
[2]Holzmann, C.A., Norton, P.G. and Tobey, M.D., ‘A graphical representation of matroids’, SIAM J. Appl. Math. 25 (1973), 618–627.CrossRefGoogle Scholar
[3]Donald, J.D., Holzmann, C.A. and Tobey, M.D., ‘A characterization of complete matroid base graphs’, J. Combin. Theory Series B 22 (1977), 139–158.CrossRefGoogle Scholar
[4]Maurer, S.B., ‘Matroid base graphs I’, J. Combin. Theory Series B 14 (1973), 216–240.CrossRefGoogle Scholar
[5]Roberts, F., Applied Combinatorics (Prentice-Hall, Englewood Cliffs, New Jersey, 1984).Google Scholar