Generic combinatorial rigidity of periodic frameworks

Generic combinatorial rigidity of periodic frameworks

We give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks. The characterization is a true analogue of the Maxwell–Laman Theorem from rigidity theory: it is stated in terms of a finite combinatorial object and the conditions are checkable by polynomial time c...

Full description

Saved in:
Bibliographic Details
Published in:Advances in mathematics (New York. 1965) Vol. 233; no. 1; pp. 291 - 331
Main Authors: Malestein, Justin, Theran, Louis
Format: Journal Article
Language:English
Published: Elsevier Inc 01-01-2013
Subjects:
Combinatorial rigidity
Matroids
Periodic graphs
Matroids
Combinatorial rigidity
Periodic graphs
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks. The characterization is a true analogue of the Maxwell–Laman Theorem from rigidity theory: it is stated in terms of a finite combinatorial object and the conditions are checkable by polynomial time combinatorial algorithms. To prove our rigidity theorem we introduce and develop periodic direction networks and Z2-graded-sparse colored graphs.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2012.10.007