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It is an open problem to find a good characterization for independence or, more generally, the rank function in the d-dimensional rigidity matroid of a graph when d \geq 3. In this paper we give a brief survey of existing lower and upper bounds on the rank of the 3-dimensional rigidity matroid of a graph and introduce a new upper bound, which may lead to the desired good characterization.
Bibtex entry:
| AUTHOR | = | {Jackson, Bill and Jord{\'a}n, Tibor}, |
| TITLE | = | {On the rank function of the 3-dimensional rigidity matroid}, |
| NOTE | = | {{\tt www.cs.elte.hu/egres}}, |
| INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
| YEAR | = | {2005}, |
| NUMBER | = | {TR-2005-09} |