TR-2020-01

A note on generic rigidity of graphs in higher dimension

Tibor Jordán



Abstract

The characterization of rigid graphs in $\R^d$ is known only in the low dimensional cases ($d=1,2$) and is a major open problem in higher dimensions. In this note we consider the other extreme case when $d$ is close to $n$, the number of vertices of the graph. It turns out that there is a fairly simple characterization as long as $n-d$ is at most four. We also characterize globally rigid graphs in this range.


Bibtex entry:

@techreport{egres-20-01,
AUTHOR = {Jord{\'a}n, Tibor},
TITLE = {A note on generic rigidity of graphs in higher dimension},
NOTE= {{\tt www.cs.elte.hu/egres}},
INSTITUTION = {Egerv{\'a}ry Research Group, Budapest},
YEAR = {2020},
NUMBER = {TR-2020-01}
}


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