## Abstract The main purpose of this paper is to show that any embedding of __K~7~__ in threeβdimensional 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.
Knots and graphs in chemistry
β Scribed by Erica Flapan
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 950 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0960-0779
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β¦ Synopsis
This paper presents a knot theoretic approach to the study of molecular graphs. It provides examples of molecular knots and links as well as other topologically complex molecules. The paper discusses various topological problems and theorems which were motivated by questions in chemistry. Some of these results have direct applications to the analysis of molecular structures, while other results, though arising out of questions about chemistry, are purely topological in nature.
π SIMILAR VOLUMES
We give a spatial representation of the complete graph K n which contains exactly ( n 6 ) Hopf links consisting of pairs of disjoint 3-cycles, where ( n 6 ) is the minimum number of pairs of disjoint 3-cycles forming a non-split link contained in any spatial representation of K n . Furthermore, we s
For a graph G, let Ξ be either the set Ξ 1 of cycles of G or the set Ξ 2 of pairs of disjoint cycles of G. Suppose that for each Ξ³ β Ξ , an embedding In this paper, we have the following three results: (1) For the complete graph K 5 on 5 vertices and the complete bipartite graph K 3,3 on 3 + 3 ver