A graph can be embedded in various spaces. This paper examines S1 embeddings of graphs. Just as links can be defined in spatial embeddings of graphs, links can be defined in S1 embeddings. Because linking properties are preserved under vertex expansion, there exists a finite complete set of minor minimal graphs such that every S1 embedding contains a non-split 3-link. This paper presents a list of minor minimal intrinsically S1 3-linked graphs, along with methods used to find and verify the list, in hopes of obtaining the complete minor minimal set. Other aspects of S1 embeddings are also examined. 1
Joel Foisy, Mathematics Department, SUNY College at Potsdamfoisyjs@potsdam.edu
Brouwer, Andrew; Davis, Rachel; Larkin, Abel; Studenmund, Daniel; and Tucker, Cherith
"Intrinsically S1 3-Linked Graphs and Other Aspects of S1 Embeddings,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 8
, Article 2.
Available at: https://scholar.rose-hulman.edu/rhumj/vol8/iss2/2