Intrinsically knotted graphs with linklessly embeddable simple minors

TL;DR

This paper constructs a new intrinsically knotted graph demonstrating that deleting or contracting an edge does not necessarily produce an intrinsically linked graph, resolving longstanding open questions.

Contribution

The authors provide a novel intrinsically knotted graph that disproves assumptions about edge deletion or contraction always leading to intrinsically linked graphs.

Findings

Existence of a new intrinsically knotted graph

Edge deletion or contraction does not always produce an intrinsically linked graph

Answers open questions in graph topology

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.