Wolfram Research

4 Dimensional Keller Graph

The Second DIMACS Implementation Challenge: 1992-1993

Originator: Panos 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["4 Dimensional Keller Graph"]
Out[1]=

Summary properties:

In[2]:=
ResourceData["4 Dimensional Keller Graph", All]["Summary"]
Out[2]=

Basic Applications

Find the maximum clique:

In[3]:=
g = ResourceData["4 Dimensional Keller Graph"];
In[4]:=
maxclique = FindClique[g]
Out[4]=

Show the maximum clique:

In[5]:=
HighlightGraph[g, Subgraph[g, maxclique], VertexCoordinates -> ReplacePart[
GraphEmbedding[g, "SpringElectricalEmbedding"], 
Thread[Map[VertexIndex[g, #]& , 
First[maxclique]] -> CirclePoints[{3., 1}, 0.6, 
Length[
First[maxclique]]]]], Sequence[
 EdgeStyle -> {Blank[] -> Opacity[0.05]}, GraphLayout -> "SpringElectricalEmbedding", VertexSize -> {Blank[] -> 0.5}]]
Out[12]=

Wolfram Research, "4 Dimensional Keller Graph" from the Wolfram Data Repository (2019) 

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