On embeddability and stresses of graphs.

Abstract  Gluck has proven that triangulated 2-spheres are generically 3-rigid. Equivalently, planar graphs are generically 3-stress free. We show that already the K 5-minor freeness guarantees the stress freeness. More generally, we prove that every K r+2-minor free graph is generically r-stress free for 1≤r≤4. (This assertion is false for r≥6.) Some further extensions are discussed. [ABSTRACT FROM AUTHOR]