On embeddability and stresses of graphs

Gluck [6] has proven that triangulated 2-spheres are generically 3-rigid. Equivalently, planar graphs are generically 3-stress free. We show that already the K5-minor freeness guarantees the stress freeness. More generally, we prove that every Kr+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.

• Type: Journal
• Year: 2007
• Where: COMBINATORICA
• Authors: Eran Nevo
• Keywords: COMBINATORICA 2007, K5-minor Freeness, Kr+2-minor Free Graph, Stress Freeness