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Second DIMACS Brockington Graph 1

The Second DIMACS Implementation Challenge: 1992-1993

Originator: Mark Brockington

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

Random graphs from Mark Brockington and Joe Culberson's generator that attempts to "hide" cliques in a graph where the expected clique size is much smaller.

Examples

Basic Examples

Retrieve the graph:

In[1]:=
ResourceData["Second DIMACS Brockington Graph 1"]
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Summary properties:

In[2]:=
ResourceData["Second DIMACS Brockington Graph 1", All]["Summary"]
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Basic Applications

Find the maximum clique:

In[3]:=
g = ResourceData["Second DIMACS Brockington Graph 1"];
In[4]:=
maxclique = FindClique[g]
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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}, 0.8, 
Length[
First[maxclique]]]]], Sequence[
 EdgeStyle -> {Blank[] -> Opacity[0.05]}, GraphLayout -> "SpringElectricalEmbedding", VertexSize -> {Blank[] -> 0.5}]]
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Wolfram Research, "Second DIMACS Brockington Graph 1" from the Wolfram Data Repository (2019) 

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