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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.

(200 vertices, 14834 edges)

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)  

Data Resource History

  • Date Created:

Source Metadata

  • Citation:
    • Volume 26, Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, October 11-13, 1993, Editors: David S. Johnson and Michael A. Trick; AMS, Providence, RI, 1996.

Data Downloads

Publisher Information

  • Prepared for the Wolfram Data Repository By: Wolfram
  • Publisher of Record: Wolfram Research