  Tait's flyping conjecture, stating that two reduced, alternating, prime link
diagrams can be connected by a finite sequence of flypes, is extended to
reduced, alternating, prime diagrams of 4-regular graphs in S^3. The proof of
this version of the flyping conjecture is based on the fact that the
equivalence classes with respect to ambient isotopy and rigid vertex isotopy of
graph embeddings are identical on the class of diagrams considered.
