Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-13T09:09:39.258Z Has data issue: false hasContentIssue false
  • English
  • Français

On ordered set systems and some conjectures related to the erdös–ko–rado theorem and turán's theorem

Part of: Combinatorics

Published online by Cambridge University Press:  26 February 2010

A. J. W. Hilton
A. J. W. Hilton
Affiliation:
The Department of Mathematics, The University of Reading, Whiteknights, Reading, England.
Get access

Extract

In [10] the following generalization of the Erdös–Ko–Rado [6] theorem was proved:

If 1 ≤ h ≤ m/2 andare r sets of h-subsets of {1,…, m} such that

then

MSC classification

Secondary: 05A20: Combinatorial inequalities
Type
Research Article
Information
Mathematika , Volume 28 , Issue 1 , June 1981 , pp. 54 - 66
Copyright
Copyright © University College London 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bermond, J. C. and Frankl, P.. “On a conjecture of Chvatal on m-intersecting hypergraphs”, Bull. London Math. Soc., 9 (1977), 310“312.CrossRefGoogle Scholar
2.Bollobás, B. and Thomason, A.. “Set colourings of graphs”, Discrete Math., 25 (1979), 21–26.CrossRefGoogle Scholar
3.Chv“tal, V.. “Problem 6” in Hypergraph Seminar, Lecture Notes in Math. 411 (Springer Verlag, 1974), 279–280.Google Scholar
4.Chvátal, V.. “An extremal set-intersection theorem”, J. London Math. Soc, 9 (1974), 355–359.CrossRefGoogle Scholar
5.Erdös, P.. “Topics in combinatorial analysis”, Proc. of the Second Louisiana Conference on Combinatorics, Graph Theory and Computing (Baton Rouge, 1971), 2–20.Google Scholar
6.Erdos, P., Ko, Chao and Rado, R.. “Intersection theorems for systems of finite sets”, Quart. J. Math. (Oxford) (2), (1961), 313–320.Google Scholar
7.Frankl, P.. “On Sperner families satisfying an additional condition”, J. Combinatorial Theory A, 20 (1976), 1–11.CrossRefGoogle Scholar
8.Fulkerson, D. R.. “Disjoint common partial transversals of two families of sets”, Studies in Pure Mathematics, Ed. Mirsky, L. (Academic Press, 1971), 107–112.Google Scholar
9.Greene, C. and Kleitman, D. J.. “Proof techniques in the theory of finite sets”, Studies in Combinatorics, M.A.A. Studies in Mathematics, Vol. 17, Ed. Rota, G. C. (1978), 22–79.Google Scholar
10.Hilton, A. J. W.. “An intersection theorem for a collection of families of subsets of a finite set”, J. London Math. Soc. (2), 15 (1977), 369–376.Google Scholar
11.Katona, G. O. H.. “A simple proof of the Erdös-Ko-Rado theorem”, J. Combinatorial Theory B, 13 (1972), 183–184.CrossRefGoogle Scholar
12.Katona, G. O. H.. “A theorem of finite sets”, Theory of Graphs, Proc. Coll. held at Tihany, 1966 (Akademai Kiado, Budapest, 1968), 187–207.Google Scholar
13.Katona, G. O. H.. “Extremal problems among subsets of a finite set”, Combinatorics, Eds. Hall, M. and van Lint, G. H., Math. Centrum Tracts 50 (Amsterdam, 1974), 13–2.Google Scholar
14.Kruskal, J. B.. “The number of simplices in a complex”, Mathematical optimization techniques (Univ. of California Press, Berkeley and Los Angeles, 1963), 251–278.CrossRefGoogle Scholar
15.Mirsky, L.. Transversal Theory (Academic Press, New York, 1971).Google Scholar
16.Turan, P.. “On an extremal problem in graph theory”, (in Hungarian), Mat. Fiz. Lapok, 48 (1941), 436–452.Google Scholar