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