How can I draw a planar graph in Mathematica?

(You): How can I draw a planar graph in Mathematica?

(Lewis): ShowGraph[]

(You): I did that with K4 and the result wasn’t planar.

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(Jonah): what do you mean by Planar. Plot[f[x],{s,low,high}]

(You): http://en.wikipedia.org/wiki/Planar_graph [http://en.wikipedia.org/wiki/Planar_graph] might be helpful.

(Jonah): sorry, can’t help you there, though, I think building a graphics function might be the best approach.

(You): there are lots of programs that will draw graphs, but I can’t find a single one that can always draw a planar graph planarly.

(Jonah): I was suggesting build a one in Mathematica

(You): Mathematica’s Combinatorica package does a lot of graph stuff, including PlanarQ[] to determine planarity, but I couldn’t find a way to force it draw planar graphs planarly. Combinatorica is huge — if it can’t draw planar graphs, I’m not sure I could write something that will.

(Jonah): Yeah, it’s possible it won’t be easy, but the power of Mathematica is that there’s almost always a way.

(You): LOL :) You want to take it on? I’ll even pay you if you do. However, it appears that this problem is NP-hard.

[Vark assigned category: planar graph, more details]

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