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5 Dimensional Keller Graph

The Second DIMACS Implementation Challenge: 1992-1993

Originator: Pnaos Pardalos

NP Hard Problems: Maximum Clique, Graph Coloring, and Satisfiability, The Second DIMACS Implementation Challenge: 1992-1993.

Graphs based on Keller's conjecture on tilings using hypercubes.

Examples

Basic Examples

Retrieve the graph:

In[1]:=
ResourceData["5 Dimensional Keller Graph"]
Out[1]=

Summary properties:

In[2]:=
ResourceData["5 Dimensional Keller Graph", All]["Summary"]
Out[2]=

Basic Applications

Show the properties of the graph:

In[3]:=
g = ResourceData["5 Dimensional Keller Graph"];
In[4]:=
Dataset[<|# -> #[g]|> & /@ {GraphDiameter, GraphDensity, MeanGraphDistance, GraphLinkEfficiency}]
Out[4]=

Wolfram Research, "5 Dimensional Keller Graph" from the Wolfram Data Repository (2019) 

Data Resource History

  • Date Created: 30 October 2019

Source Metadata

  • Citation:
    • "Keller's Cube-Tiling Conjecture is False in High Dimensions," J.C. Lagarias and P.W. Shor, Bulletin of the AMS, 27: 279-283 (1992).

Data Downloads

Publisher Information

  • Contributed By: Wolfram
  • Publisher of Record: Wolfram Research