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 |
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ページ(範囲) | 87-109 |
ページ数 | 23 |
ジャーナル | Topology and its Applications |
巻 | 112 |
号 | 1 |
DOI | |
出版ステータス | Published - 2001 |
外部発表 | はい |
ASJC Scopus subject areas
- Geometry and Topology