G(10,30): A Minor-Minimal Intrinsically Knotted Graph
Date of Award
Dr. Andrei Pavelescu
Dr. Elena Pavelescu, Dr. Martin Frank, Dr. Gayan Abeynanda
In this paper, we shall lay the groundwork for a proof of the minor-minimal intrinsic knotting of the graph G(10, 30). We show that this graph is in fact minor minimal with respect to the property of intrinsic knotting, i.e that no minor of G(10, 30) is intrinsically knotted. Moreover, we discuss the procedure for showing that G(10, 30) itself is intrinsically knotted, and provide a collection of subgraphs that can be used to aid in a proof. In this way, we hope to contribute to the growing list of known minor-minimal intrinsically knotted graphs.
Herron, Johanthan R., "G(10,30): A Minor-Minimal Intrinsically Knotted Graph" (2023). Theses and Dissertations. 128.