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Boxes in Rn —A ‘Fractional’ Theorem

Published online by Cambridge University Press:  20 November 2018

Meir Katchalski
Meir Katchalski*
Affiliation:
Technion—I. I. T., Haifa, Israel
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A box in Euclidean 𝓀-dimensional space Rk is a set of the type

A family of boxes, unless stated otherwise, is finite.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 4 , April 1980 , pp. 831 - 838
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Abbott, H. and Katchalski, M., A Turàn type problem for interval graphs, Discrete Math. 25 (1979), 85–88.Google Scholar
2. Berge, C., Graphs et hypergraphs (Dunod, Paris, 1970).Google Scholar
3. Danzer, L., Grünbaum, B. and Klee, V., Helly's theorem and its relatives, Proc. Symp. Pure Math., AMS 7 (1963), 100–181.Google Scholar
4. Erdös, P., On a theorem of Rademacher Turàn, Illinois J. Math. 6 (1962), 122–136.Google Scholar
5. Grünbaum, B., Convex polytopes (Interscience, London, 1967).Google Scholar
6. Harary, F., Graph theory (Addison-Wesley, Reading, Mass., 1960).Google Scholar
7. Helly, E., Über Mengen konvexer Körper mit gemeinschaftlichen Punkten, Jber. Deutsch. Math. Verein. 32 (1923), 175–176.Google Scholar
8. Katchalski, M. and Liu, A., A problem of geometry in Rn , Proc. A.M.S. 75 (1979), 284–288.Google Scholar
9. Lekkerkerker, C. G. and Boland, J. C., Representation of a finite graph by a set of intervals on the real line, Fund. Math. 51 (1962), 45–64.Google Scholar
10. Turán, P., Eine Extremalaufgabe aus der Graphen Théorie, Mat. Fiz. Lapok. 48 (1941), 436–452.Google Scholar