The Y-triangle move does not preserve Intrinsic Knottedness

TL;DR

This paper demonstrates that the Y-triangle move can alter a graph's intrinsic knottedness, providing a counterexample to previous assumptions about move preservation.

Contribution

It presents the first explicit example showing the Y-triangle move does not preserve intrinsic knottedness, challenging prior beliefs.

Findings

Y-triangle move does not preserve intrinsic knottedness

Constructed a counterexample from K_7

Shows the move can change graph properties

Abstract

We answer the question "Does the Y-triangle move preserve intrinsic knottedness?" in the negative by giving an example of a graph that is obtained from the intrinsically knotted graph K_7 by triangle-Y and Y-triangle moves but is not intrinsically knotted.