Published in:
Let $G=(V,E)$ be a graph and $u,v\in V$ be two distinct vertices. We give a necessary and sufficient condition for the existence of an infinitesimally rigid two-dimensional bar-and-joint framework $(G,p)$, in which the positions of $u$ and $v$ coincide. We also determine the rank function of the corresponding modified generic rigidity matroid on ground-set $E$. The results lead to efficient algorithms for testing whether a graph has such a coincident realization with respect to a designated vertex pair and, more generally, for computing the rank of $G$ in the matroid.
Bibtex entry:
AUTHOR | = | {Fekete, Zsolt and Jord{\'a}n, Tibor and Kaszanitzky, Vikt{\'o}ria}, |
TITLE | = | {Rigid two-dimensional frameworks with two coincident points}, |
NOTE | = | {{\tt egres.elte.hu}}, |
INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
YEAR | = | {2012}, |
NUMBER | = | {TR-2012-08} |