Realization of knots and links in a spatial graph

研究成果: Article査読

24 被引用数 (Scopus)

抄録

For a graph G, let Γ be either the set Γ2 of cycles of G or the set Γ2 of pairs of disjoint cycles of G. Suppose that for each γ ε Γ, an embedding φγ : γ → S3 is given. A set {φγ \ γ ε Γ) is realizable if there is an embedding f : G → S3 such that the restriction map f\γ is ambient isotopic to φγ for any γ ε Γ. A graph is adaptable if any set {φγ \ γ ε Γ1] is realizable. In this paper, we have the following three results: (1) For the complete graph K5 on 5 vertices and the complete bipartite graph K3,3 on 3 + 3 vertices, we give a necessary and sufficient condition for {φγ \ γ ε Γ1} to be realizable in terms of the second coefficient of the Conway polynomial. (2) For a graph in the Petersen family, we give a necessary and sufficient condition for {φγ | γ ε Γ2) to be realizable in terms of the linking number. (3) The set of non-adaptable graphs all of whose proper minors are adaptable contains eight specified planar graphs.

本文言語English
ページ(範囲)87-109
ページ数23
ジャーナルTopology and its Applications
112
1
DOI
出版ステータスPublished - 2001
外部発表はい

ASJC Scopus subject areas

  • Geometry and Topology

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