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Combinatorica

, Volume 4, Issue 4, pp 345–349 | Cite as

On combinatorial properties of spheres in euclidean spaces

  • Vojtěch Rödl
Article

Abstract

For λ>√2 there exists a triangle-free graphG such that for nod canG be imbedded into thed-dimensional unit sphere with two points joined if and only if their distance is >λ.

AMS subject classification (1980)

05 C 99 51 N 20 

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References

  1. [1]
    B. Alspach, M. Rosenfeld, On embedding triangle-free graphs in unit spheres,Discrete Math.,19 (1977), 103–111.zbMATHCrossRefMathSciNetGoogle Scholar
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    P. Erdős, F. Galvin, A. Hajnal, On set-systems having large chromatic number and not containing prescribed subsystems,Infinite and Finite Sets (A. Hajnal, R. Rado and V. T. Sós eds.) Budapest, Hungary 1975, 425–514.Google Scholar
  3. [3]
    D. C. Larman, A Triangle Free Graph Which Cannot be √3-imbedded in any Euclidean Unit Sphere,Journal of Combinatorial Theory, (A) 24 (1978), 162–169.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    F. P. Ramsey, On a Problem of Formal Logic,Proc. of the London Math. Soc. (2) 30 (1930), 264–286.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó 1984

Authors and Affiliations

  • Vojtěch Rödl
    • 1
  1. 1.Dept. of MathematicsFJFI ČVUTPraha, 1ČSSR

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