✦ LIBER ✦

Intrinsically knotted graphs

✍ Scribed by Joel Foisy

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 100 KB
Volume: 39
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10017

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In 1983, Conway and Gordon [J Graph Theory 7 (1983), 445–453] showed that every (tame) spatial embedding of K~7~, the complete graph on 7 vertices, contains a knotted cycle. In this paper, we adapt the methods of Conway and Gordon to show that K~3,3,1,1~ contains a knotted cycle in every spatial embedding. In the process, we establish that if a graph satisfies a certain linking condition for every spatial embedding, then the graph must have a knotted cycle in every spatial embedding. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 178–187, 2002; DOI 10.1002/jgt.10017

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