List of problems that are in general NP-hard but have polynomial-time solution in planar graphs?

Question

I encountered many problems that can be formulated as graph problem. It is in general NP-hard but sometimes the graph can be proved to be planar. Hence, I am interested in learning these problems and the algorithms.

So far as I know:

Max cut in planar graphs
Four-coloring in planar graphs
Max Independent Set in cubic planar graphs

Hope someone can complete this list.

Looking at their [FAQ](http://cstheory.stackexchange.com/faq), I think cstheory.se would probably close this. — Bill the Lizard, Jun 22 '11 at 00:49
I had closed this because it seems like a "List of X" question, but I'm reopening in hopes that there's one resource with the answer. If others feel there's no one right answer they can vote to close. — Bill the Lizard, Jun 22 '11 at 00:59

score 3 · Accepted Answer · answered Jun 29 '11 at 22:45

3

In this compendium of NP-complete problems, under planar in the index there are a good number (~25) of entries. These entries typically link to problems where planar input admits a PTAS.

answered Jun 29 '11 at 22:45

borrible

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List of problems that are in general NP-hard but have polynomial-time solution in planar graphs?

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