Intrinsic 3-linkedness is Not Preserved by $\text{Y}\nabla$ moves

TL;DR

This paper constructs new intrinsically 3-linked graphs and demonstrates that the property of intrinsic 3-linkedness is not preserved under Y∇ moves, providing new insights into graph transformations.

Contribution

It introduces five new constructions of intrinsically 3-linked graphs and proves that Y∇ moves do not preserve intrinsic 3-linkedness.

Findings

Y∇ moves can destroy intrinsic 3-linkedness

New intrinsically 3-linked graphs are constructed

Intrinsic 3-linkedness is not invariant under certain graph transformations

Abstract

This paper introduces a number of new intrinsically 3-linked graphs through five new constructions. We then prove that intrinsic 3-linkedness is not preserved by $\text{Y}\nabla$ moves. We will see that the graph $M$, which is obtained through a $\text{Y}\nabla$ move on $(PG)^*_*(PG)$, is not intrinsically 3-linked.