Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T10:41:10.200Z Has data issue: false hasContentIssue false

Boxes in Rn —A ‘Fractional’ Theorem

Published online by Cambridge University Press:  20 November 2018

Meir Katchalski*
Affiliation:
Technion—I. I. T., Haifa, Israel
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A box in Euclidean 𝓀-dimensional space Rk is a set of the type

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

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Abbott, H. and Katchalski, M., A Turàn type problem for interval graphs, Discrete Math. 25 (1979), 8588.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), 100181.Google Scholar
4. Erdös, P., On a theorem of Rademacher Turàn, Illinois J. Math. 6 (1962), 122136.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), 175176.Google Scholar
8. Katchalski, M. and Liu, A., A problem of geometry in Rn , Proc. A.M.S. 75 (1979), 284288.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), 4564.Google Scholar
10. Turán, P., Eine Extremalaufgabe aus der Graphen Théorie, Mat. Fiz. Lapok. 48 (1941), 436452.Google Scholar