OFFSET
3,4
COMMENTS
A graph G=(V,E) is (3,6)-tight if |E|=3|V|-6 and for every subgraph G'=(V',E') with at least 3 vertices |E'|<=3|V'|-6.
Every minimally rigid graph in 3D (A328419) is (3,6)-tight.
REFERENCES
A. Nixon and E. Ross, Inductive Constructions for Combinatorial Local and Global Rigidity, pages 413-434 of M. Sitharam, A. St. John and J. Sidman, editors, Handbook of Geometric Constraint System Principles, CRC Press, 2019.
LINKS
Georg Grasegger, Dataset of (3,6)-tight graphs
Martin Larsson, Nauty Laman plugin
EXAMPLE
The triangle graph and the tetrahdral graph are (3,6)-tight.
PROG
(nauty with Laman plugin) gensparseg $n -K3 #see link
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Georg Grasegger, Sep 16 2024
EXTENSIONS
a(12)-a(13) added by Georg Grasegger, Oct 17 2024
STATUS
approved