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Knots and links in spatial graphs
Author(s) -
Conway J. H.,
McA. Gordon C.
Publication year - 1983
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.3190070410
Subject(s) - mathematics , embedding , combinatorics , disjoint sets , euclidean space , euclidean geometry , space (punctuation) , argument (complex analysis) , discrete mathematics , geometry , computer science , biochemistry , chemistry , artificial intelligence , operating system
The main purpose of this paper is to show that any embedding of K 7 in three‐dimensional euclidean space contains a knotted cycle. By a similar but simpler argument, it is also shown that any embedding of K 6 contains a pair of disjoint cycles which are homologically linked.