On embeddability and stresses of graphs

Eran Nevo

doi:10.1007/s00493-007-2168-x

On embeddability and stresses of graphs

Eran Nevo^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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.

Original language	English
Pages (from-to)	465-472
Number of pages	8
Journal	Combinatorica
Volume	27
Issue number	4
DOIs	https://doi.org/10.1007/s00493-007-2168-x
State	Published - Jul 2007

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title = "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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AB - 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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On embeddability and stresses of graphs

Abstract

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