Marble graphs with various rigidity properties

This dataset contains examples of graphs comparing rigidity concepts for generic bar-joint frameworks and for marble graphs. A marble graph is the contact graph of a collection of unit spheres in dimension three with non-overlapping interiors. For each graph there is a Graph6 file format and a list of edges in Mathematica notation. We also provide the coordinates that give the unit-distances (also in Mathematica format). The names of the files indicate the rigidity properties of the given graph.

G.G. was partially supported by the Austrian Science Fund (FWF): 10.55776/P31888 and 10.55776/I6233. K.K. was partially supported by the Academy of Finland grant number 323416. F.M. was partially supported by the FWO grants G0F5921N and G023721N, the KU Leuven iBOF/23/064 grant, and the UiT Aurora MASCOT project. A.N. was partially supported by EPSRC grant number EP/W019698/1.

Country

Finland

Related Organizations

University of Bristol
United Kingdom
Austrian Academy of Sciences
Austria
Johann Radon Institute for Computational and Applied Mathematics
Austria
KU Leuven
Belgium
Aalto University
Finland

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Keywords

marble graph, rigidity

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