# Rigidity for sticky disks

 Authors: Robert Connelly, Steven J. Gortler, and Louis Theran Preprint: 1809.02006, 2018 Full text: arXiv

In this paper, we prove that any packing of $n$ disks with generic radii can have at most $2n - 3$ disk pairs in contact. If we do not allow any of the existing contacts to be broken (modeling a collection of sticky disks), then the packing is rigid iff it has exactly $2n - 3$ contacts. Thus we obtain a Laman-like characterization of rigidity for sticky disks under a generic radii assumption.