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Is there any way to tell Mathematica to generate a list of graphs that are both traceable and planar?

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Check GraphData.

Get a list of names with this command:

Intersection[
 GraphData["Planar"],
 GraphData["Traceable"]
]

Apply GraphData to a name to get the graph.

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  • $\begingroup$ This is awesome, thanks! $\endgroup$ – Juan Jan 26 '16 at 8:52

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