A Proof Using Böhme's Lemma That no Petersen Family Graph has a Flat Embedding
Year: 2024
Type: article
Abstract: Sachs and Conway-Gordon used linking number and a beautiful counting argument to prove that every graph in the Petersen family is intrinsically linked (have a pair of disjoint cycles that form a nonsplit link in every spatial embedding) and thus each family member has no flat spatial embedding (an embedding for which every cycle bounds a disk with interior disjoint from the graph). We give an alternate proof that every Petersen family graph has no flat embedding by applying Böhme's Lemma and the Jordan-Brouwer Separation Theorem.
Authors: Joel Foisy, Catherine Jacobs, Trinity Paquin, Morgan Schalizki, Henry Stringer
Institutions: State University of New York at Potsdam, Wellesley College
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: National Security Agency
OpenAlex ID: W4405016940