TRIANGLE-Y EXCHANGES ON INTRINSIC KNOTTING OF ALMOST COMPLETE AND COMPLETE PARTITE GRAPHS
Li Yang, Jiahu Qin, Fengchun Lei, Xiangke Wang, Xihai Zhang · Journal of Knot Theory and Its Ramifications · 2011
Let G be a 0- or 1-deficient graph which is intrinsically knotted, let J represent any graph obtained from G by a finite sequence of Δ-Y exchanges and/or vertex expansions. We prove that removing any vertex of J, and all edges incident to that vertex, yields an intrinsically linked graph. This result provides more intrinsically knotted graphs which satisfy the conjecture mentioned in Adams' The Knot Book that removing any vertex from an intrinsically knotted graph yields an intrinsically linked graph.