GRAPHS WITH DISJOINT LINKS IN EVERY SPATIAL EMBEDDING
STEPHAN CHAN, Anton Dochtermann, Joel Foisy, JENNIFER HESPEN, EMAN KUNZ, TRENT LALONDE, Quincy Loney, KATHERINE SHARROW, Nathan Thomas · Journal of Knot Theory and Its Ramifications · 2004
We exhibit a graph, G12, that in every spatial embedding has a pair of non-splittable 2 component links sharing no vertices or edges. Surprisingly, G12does not contain two disjoint copies of graphs known to have non-splittable links in every embedding. We exhibit other graphs with this property that cannot be obtained from G12by a finite sequence of Δ-Y and/or Y-Δ exchanges. We prove that G12is minor minimal in the sense that every minor of it has a spatial embedding that does not contain a pair of non-splittable 2 component links sharing no vertices or edges.