Published February 16, 2024 | Version v1
Dataset Open

Non-planar apex graphs with different independence properties

Authors/Creators

  • 1. Austrian Academy of Sciences
  • 2. ROR icon University of Bristol
  • 3. ROR icon Lancaster University
  • 4. ROR icon Worcester Polytechnic Institute

Description

In this data set we provide the list of non-planar connected graphs with different apex properties. We call a graph apex if there is a vertex whose deletion gives a planar graph. Independence is considered in the 3-dimensional generic rigidity matroid. A graph is (3,6)-sparse if if for every subset of n vertices,
with at least 3 elements, the number of edges in the subgraph induced by these elements is at most 3n − 6.

The data set provides graphs in Graph6 data format.

Files

NonPlanarDependentApexGraphsV6-10.zip

Files (49.0 MB)

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md5:3984d4e1f4db7691a84bc2821b1e0a35
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Additional details

Funding

FWF Austrian Science Fund
Realizations of Rigid Graphs 10.55776/P31888
UK Research and Innovation
The graph rigidity problem in arbitrary dimension EP/X036723/1
FWF Austrian Science Fund
Paradoxical flexibility of frameworks I 6233
FWF Austrian Science Fund
Paradoxical flexibility of frameworks I 6233