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Steiner Triple System A9 Graph

The Second DIMACS Implementation Challenge: 1992-1993

Originator: Carlo Mannino

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

Clique formulation of the Steiner Triple Problem, translated from the set covering formulation.

Examples

Basic Examples

Retrieve the graph:

In[1]:=
ResourceData["Steiner Triple System A9 Graph"]
Out[1]=

Summary properties:

In[2]:=
ResourceData["Steiner Triple System A9 Graph", All]["Summary"]
Out[2]=

Basic Applications

Find the maximum clique:

In[3]:=
g = ResourceData["Steiner Triple System A9 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[{2.7, 0.9}, 0.5, 
Length[
First[maxclique]]]]], Sequence[
 EdgeStyle -> {Blank[] -> Opacity[0.05]}, 
  GraphLayout -> "SpringElectricalEmbedding", 
  VertexSize -> {Blank[] -> 0.5}]]
Out[6]=

Wolfram Research, "Steiner Triple System A9 Graph" from the Wolfram Data Repository (2019) 

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