EDGE-HOMOTOPY CLASSIFICATION OF SPATIAL COMPLETE GRAPHS ON FOUR VERTICES
Ryo Nikkuni · Journal of Knot Theory and Its Ramifications · 2004
Two spatial embeddings of a graph are said to be edge-homotopic if they are transformed into each other by self-crossing changes and ambient isotopies. We show that two spatial embeddings of the complete graph on four vertices are edge-homotopic if and only if they have the same α-invariant.