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.

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Correspondence to Eran Nevo.

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Supported by an I.S.F. grant.

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Nevo, E. On embeddability and stresses of graphs. Combinatorica 27, 465–472 (2007). https://doi.org/10.1007/s00493-007-2168-x

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Mathematics Subject Classification (2000)

  • 52C25
  • 05C83