, Volume 22, Issue 1, pp 149-158

Spatial Graphs and Oriented Matroids: the Trefoil

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Abstract.

Let m=m(K) be the smallest positive integer such that every linear spatial representation 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.

Received July 8, 1997, and in revised form January 16, 1998.