Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bound for the rank of rigidity matrix of 4-valent graphs under
  various connectivity assumptions   In this paper we study the rank of planar rigidity matrix of 4-valent graphs,
both in case of generic realizations and configurations in general position,
under various connectivity assumptions on the graphs. For each case considered,
we prove a lower bound and provide an example which shows the order of the
bound we proved is sharp. This work is closed related to work in
\cite{Luo:Rigidity} and answers some questions raised there.

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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex