# lec12 - • Edge Addition: Take any 2 vertices without any...

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Geometric Constraints April 13 Connected Rigidity Matroids and Unique Realization of Graphs Seminar by Yong Zhou April 14, 2006 Deﬁnitions: Global Rigidity: Generically has a unique realization. Connected Matroid: Matroid M is connected if it has atleast 2 ele- ments and only one component. Circuit/Cycle: Removal of an edge will give the maximal independent set. Node: is a vertex with degree 3. Feasible Node: A node V is said to be feasible if G v is a brick for some splitting G v of G at V. Splitting: Inverse operation of 1-extension 1-extension: The same as in previous discussions.

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Unformatted text preview: • Edge Addition: Take any 2 vertices without any edges and just put an edge between them. • Redundantly Rigid/2-Rigid: Removing any one edge still leaves the graph Rigid. 1 Consider the following Statements 1. G is d+1 Connected 2. G is 2-Rigid 3. G can be obtained from K 4 by extensions. 4. G is globally rigid. Some observations on these statements • 2 implies 3 and 3 implies 2, The ﬁrst implication is shown in Theorem 6.1 in the paper. The second implication is shown in Lem 3.9 of the paper. to be continued . .. 2...
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## This note was uploaded on 11/09/2011 for the course CIS 6930 taught by Professor Staff during the Fall '08 term at University of Florida.

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lec12 - • Edge Addition: Take any 2 vertices without any...

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