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Intrinsically knotted graphs
Author(s) -
Foisy Joel
Publication year - 2002
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.10017
Subject(s) - embedding , combinatorics , graph , mathematics , book embedding , discrete mathematics , graph theory , graph embedding , computer science , line graph , 1 planar graph , artificial intelligence
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