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Wed 19 Oct, 2005 01:37 pm
By placing the vertices at the points (1, 1^2, 1^3), (2, 2^2, 2^3),
(3, 3^2, 3^3), . . . , prove that any simple graph can be drawn without crossings in the Euclidean three-dimensional space so that each edge is represented by a straight line.
What is this all about???
Still stuck on this. Anyone???
The maximal dimension of the figure that three points span is 2, i.e., three points can span at most a plane.
satt_fs wrote:The maximal dimension of the figure that three points span is 2, i.e., three points can span at most a plane.
Yes, but there are infinitely many points here, all of the form
(k, k^2, k^3). Doesn't stop with just three of them. Besides, I don't see the connection between what you said and what the problem asks... how do we prove the result for simple graphs? Thanks!
satt_fs wrote:The maximal dimension of the figure that three points span is 2, i.e., three points can span at most a plane.
Yes, but there are infinitely many points here, all of the form
(k, k^2, k^3). Doesn't stop with just three of them. Besides, I don't see the connection between what you said and what the problem asks... how do we prove the result for simple graphs? Thanks!
satt_fs wrote:The maximal dimension of the figure that three points span is 2, i.e., three points can span at most a plane.
Yes, but there are infinitely many points here, all of the form
(k, k^2, k^3). Doesn't stop with just three of them. Besides, I don't see the connection between what you said and what the problem asks... how do we prove the result for simple graphs? Thanks!
satt_fs wrote:The maximal dimension of the figure that three points span is 2, i.e., three points can span at most a plane.
Yes, but there are infinitely many points here, all of the form
(k, k^2, k^3). Doesn't stop with just three of them. Besides, I don't see the connection between what you said and what the problem asks... how do we prove the result for simple graphs? Thanks!
satt_fs wrote:The maximal dimension of the figure that three points span is 2, i.e., three points can span at most a plane.
Yes, but there are infinitely many points here, all of the form
(k, k^2, k^3). Doesn't stop with just three of them. Besides, I don't see the connection between what you said and what the problem asks... how do we prove the result for simple graphs? Thanks!
I know very little about graph theory but I would imagine you might need to prove that all vectors connecting points of the form ( k, k^2, k^3 )are "linearly independent", for otherwise would they not cross or coincide ?
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