TR-2009-08

Generically globally rigid zeolites in the plane

Tibor Jordán

Published in:
Information Proc. Letters, Vol. 110, Issues 18-19, 2010, Pages 841-844.

A d-dimensional zeolite is a d-dimensional body-and-pin framework with a (d+1)-regular underlying graph G. That is, each body of the zeolite is incident with d+1 pins and each pin belongs to exactly two bodies. The corresponding d-dimensional combinatorial zeolite is a bar-and-joint framework whose graph is the line graph of G.
 
We show that a two-dimensional combinatorial zeolite is generically globally rigid if and only if its underlying 3-regular graph G is 3-edge-connected. The proof is based on a new rank formula for the two-dimensional rigidity matroid of line graphs.

Bibtex entry:

@techreport{egres-09-08,

AUTHOR	=	{Jord{\'a}n, Tibor},
TITLE	=	{Generically globally rigid zeolites in the plane},
NOTE	=	{{\tt egres.elte.hu}},
INSTITUTION	=	{Egerv{\'a}ry Research Group, Budapest},
YEAR	=	{2009},
NUMBER	=	{TR-2009-08}

}