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Some applications of a theorem of Rado

Published online by Cambridge University Press:  26 February 2010

D. J. A. Welsh
D. J. A. Welsh
Affiliation:
Merton College, Oxford, and The University of Michigan
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Extract

It has been shown by Mirsky and Perfect [1] that the theorem of Rado [2], linking matroid theory and transversal theory, has important applications in combinatorial theory. In this note I use it to obtain necessary and sufficient conditions for two families of sets to have a common transversal containing a given set, and then I show how it may be used to obtain a variant of a well-known theorem that was obtained by Hoffman and Kuhn [3] using linear programming methods.

Type
Research Article
Information
Mathematika , Volume 15 , Issue 2 , December 1968 , pp. 199 - 203
Copyright
Copyright © University College London 1968

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References

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