Intrinsic Knotting of Almost Complete Partite Graphs (Communications in Mathematical Research, 2021)
Let $G$ be a complete $p$-partite graph with 2 edges removed, $p ≥ 7$, which isintrinsically knotted. Let $J$ represent any graph obtained from $G$ by a finite sequenceof $∆-Y$ exchanges and/or vertex expansions. In the present paper, we show thatthe removal of any vertex of $J$ and all edges incident to that vertex produces anintrinsically linked graph. This result offers more intrinsically knotted graphs whichhold for the conjecture presented in Adams' book (Adams C. The Knot Book. NewYork: W. H. Freeman and Company, 1994), that is, the removal of any vertex froman intrinsically knotted graph yields an intrinsically linked graph.