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Intrinsically knotted graphs with linklessly embeddable simple minors

Thomas W Mattman, Ramin Naimi, Andrei Pavelescu and Elena Pavelescu

Algebraic & Geometric Topology 24 (2024) 1203–1223
Abstract

It has been an open question whether the deletion or contraction of an edge in an intrinsically knotted graph always yields an intrinsically linked graph. We present a new intrinsically knotted graph that shows the answer to both questions is no.

Keywords
spatial graph, intrinsic knotting, intrinsic linking, Colin de Verdière invariant
Mathematical Subject Classification
Primary: 05C10
Secondary: 57M15, 57K10
References
Publication
Received: 18 May 2022
Accepted: 11 October 2022
Published: 12 April 2024
Authors
Thomas W Mattman
Department of Mathematics and Statistics
California State University at Chico
Chico, CA
United States
http://tmattman.yourweb.csuchico.edu
Ramin Naimi
Department of Mathematics
Occidental College
Los Angeles, CA
United States
http://faculty.oxy.edu/rnaimi/
Andrei Pavelescu
Mathematics and Statistics Department
University of South Alabama
Mobile, AL
United States
http://apaveles.wixsite.com/scientist-site
Elena Pavelescu
Mathematics and Statistics Department
University of South Alabama
Mobile, AL
United States

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