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LINKING IN STRAIGHT-EDGE EMBEDDINGS OF K₇

LEWIS D. LUDWIG

Department of Math and Computer Science, Denison University, Granville, OH 43023, USA

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and

PAMELA ARBISI

Department of Math and Computer Science, Denison University, Granville, OH 43023, USA

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https://doi.org/10.1142/S0218216510008467Cited by:2 (Source: Crossref)

Abstract

In 1983 Conway and Gordon and Sachs proved that every embedding of the complete graph on six vertices, K₆, is intrinsically linked. In 2004 it was shown that all straight-edge embeddings of K₆ have either one or three linked triangle pairs. We expand this work to characterize the straight-edge embeddings of K₇ and determine the number and types of links in every embedding which forms a convex polyhedron of seven vertices.

Keywords:

AMSC: 57M15, 57M25

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