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A Matroid Reconstruction Result

Published online by Cambridge University Press:  12 September 2008

Allan D. Mills
Allan D. Mills
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803, U.S.A.
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Abstract

Suppose M and N are distinct matroids on a set E such that, for every e ∈ E, the deletion of e from M equals the deletion of e from N or the contraction of e from M equals the contraction of e from N. In this note we prove that, apart from some easily specified exceptions, one of M and N must be a relaxation of the other.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 3 , September 1994 , pp. 371 - 373
Copyright
Copyright © Cambridge University Press 1994

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References

[1]Kahn, J. (1985) A problem of P. Seymour on nonbinary matroids. Combinatorica 5 319–323.CrossRefGoogle Scholar
[2]Oxley, J. G. (1992) Matroid Theory, Oxford University Press, New York.Google Scholar