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

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.