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Remarks on Dilworth's theorem in relation to transversal theory

Published online by Cambridge University Press:  18 May 2009

Hazel Perfect
Hazel Perfect
Affiliation:
University of Sheffield
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In his book Transversal Theory [3], L. Mirsky has remarked that “At present, the relation between Dilworth's decomposition theorem…and transversal theory is rather tenuous; but further study may reveal unexpected connections”. Some of these connections can perhaps now be seen a little more clearly; and our purpose in this note is to make one or two observations in this regard. Throughout, all sets considered are finite.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 19 - 22
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCES

1.Dilworth, R. P., A decomposition theorem for partially ordered sets, Ann. of Math. (2) 51 (1950), 161–166.CrossRefGoogle Scholar
2.König, D., Theorie der endlichen und unendlichen Graphen (Leipzig, 1936).Google Scholar
3.Mirsky, L., Transversal theory (Academic Press, 1971).Google Scholar
4.Perfect, H., Remark on a criterion for common transversals, Glasgow Math. J. 10 (1969), 66–67.Google Scholar
5.Perfect, H., Marginal elements in transversal theory, Studies in Pure Mathematics (Ed. Mirsky, L., Academic Press, 1971).Google Scholar
6.Perles, M. A., A proof of Dilworth's decomposition theorem for partially ordered sets, Israel J. Math. 1 (1963), 105–107.Google Scholar
7.Tverberg, H., On Dilworth's decomposition theorem for partially ordered sets, J. Combinational Theory 3 (1967), 305–306.Google Scholar