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Uniqueness of an independent transversal of a family of sets†

Published online by Cambridge University Press:  24 October 2008

Richard A. Brualdi
Richard A. Brualdi
Affiliation:
University of Wisconsin, Madison, Wisconsin, 53706 U.S.A.
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Extract

In his book Transversal Theory (4) Mirsky introduces the problem of finding a necessary and sufficient condition in order that a finite family of sets have a unique independent transversal. The purpose of this note is to give one necessary and sufficient condition. More generally, we give a necessary and sufficient condition in order that a common basis of two rank-finite matroids be unique. We then specialize this result to give an answer to the above question.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 3 , November 1972 , pp. 375 - 380
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

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