Discrete & Computational Geometry

, Volume 22, Issue 1, pp 149–158

Spatial Graphs and Oriented Matroids: the Trefoil


  • J. L. Ramirez Alfonsin
    • Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Cientifica, Circuito Exterior C.U., Mexico D.F. 04510

DOI: 10.1007/PL00009446

Cite this article as:
Ramirez Alfonsin, J. Discrete Comput Geom (1999) 22: 149. doi:10.1007/PL00009446


Let m=m(K) be the smallest positive integer such that every linearspatialrepresentation of the complete graph with n vertices, n ≥ m , contains either the knot K or its mirror . In this paper we show that m(Trefoil)=7 . The proof uses the theory of oriented matroids.

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