Re: [math-fun] Geometry/topology question about planar graphs
Thanks to all who responded to this question! Still a mystery to me is this: Given a graph G embedded in the plane, under what circumstances can a straight-line version of G be obtained through a continuous deformation of the original embedding, through embeddings ? --Dan
Still a mystery to me is this: Given a graph G embedded in the plane, under what circumstances can a straight-line version of G be obtained through a continuous deformation of the original embedding, through embeddings ?
--Dan
Do you have an example where it's not possible?
On Wed, 4 Jun 2003, Edwin Clark wrote:
Still a mystery to me is this: Given a graph G embedded in the plane, under what circumstances can a straight-line version of G be obtained through a continuous deformation of the original embedding, through embeddings ?
--Dan
Do you have an example where it's not possible?
I'm sure it's quite easy to prove it's always possible. However, the "Carpenter's Ruler" problem (are the plane embeddings of a hinged ruler interconvertible in this way, keeping the segment-lengths fixed) is quite difficult - indeed I think it's still unsolved, and the corresponding assertion for arbitary graphs is false. John conway
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asimovd＠aol.com -
Edwin Clark -
John Conway