Realization of knots and links in a spatial graph

✍ Scribed by Kouki Taniyama; Akira Yasuhara

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 373 KB
• Volume: 112
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00228-x

✦ Synopsis

For a graph G, let Γ be either the set Γ 1 of cycles of G or the set Γ 2 of pairs of disjoint cycles of G. Suppose that for each γ ∈ Γ , 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 vertices, we give a necessary and sufficient condition for {φ γ | γ ∈ Γ 1 } 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 {φ γ | γ ∈ Γ 2 } 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.