Mathematical Sciences Department Discrete Math Seminar
Marie Kramer, Syracuse University
Monday, April 7th
3:00pm - 4:00 pm
Title: On the embeddability of small cubic graphs into the torus
Abstract: While obstructions to embedding graphs into the plane and the real projective plane are well understood, there is no known complete list for other surfaces, such as the torus or the Klein bottle. Moreover, the embeddability of planar obstructions into other surfaces has been studied: Mohar and Gagarin, Kocay, and Neilson classified such embeddings into the real projective plane and the torus, respectively. In this talk, we will discuss a similar result classifying the embeddings of the six cubic projective plane obstructions into the torus. We will show how this result helped us verify Chambers’ computer assisted results regarding cubic torus obstructions with small first Betti number. Lastly, we will highlight a connection between the existence of embeddings of graphs into certain surfaces and geometric data of special torus representations found by Kennard, Wiemeler, and Wilking.