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bio website gilkalai.wordpress.com
location Jerusalem
age 59
visits member for 5 years, 1 month
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Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University

Dec
4
comment Generalizations of Planar Graphs
One generalization that Kristal point out to is graphs that can be embedded in a given surface. This is perhaps the most studied generalization of planar graphs. Going to higher dimensional objects was suggested by Alon (embeddability of k spaces into R^2k.) Kristal's suggestion to replace the ambient space by other spaces is certainly interesting. If I remember correctly embeddability of k manifolds in Euleriam 2k-manifolds (2k-manifolds with Euler characteristic 2) is equivalent to embeddability in R^{2k}. (OK, maybe the condition is vanishing middle homology and not being Eulerian.)
Dec
4
comment Generalizations of Planar Graphs
That's a very nice idea!
Dec
4
revised Why are planar graphs so exceptional?
grammer
Dec
3
comment Generalizations of Planar Graphs
I think that embeddability of 2 dimensional spaces into R^4 is the most difficult case.
Dec
3
comment Generalizations of Planar Graphs
Muktiple answers/posts are welcomed. I hope we can have a useful source.
Dec
3
comment Generalizations of Planar Graphs
Dear Alon, this is a very important and interesting generalization.
Dec
3
revised Generalizations of Planar Graphs
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Dec
3
asked Generalizations of Planar Graphs
Dec
2
answered What are the most overloaded words in mathematics?
Dec
1
revised Minkowski sum of small connected sets
edited tags
Dec
1
comment Why are planar graphs so exceptional?
That's interesting. I was not aware of it; So is the statement that every graph can be realized by a circle packing on arbitrary surface? (with a Riemannian metric?) Is there also uniqueness results like in the planar case?
Dec
1
comment Fundamental Examples
Is it possible? Is it moral?
Dec
1
answered Fundamental Examples
Dec
1
revised Why are planar graphs so exceptional?
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Dec
1
revised Why are planar graphs so exceptional?
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Dec
1
revised Why are planar graphs so exceptional?
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Nov
30
revised Fundamental Examples
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Nov
30
accepted How Does Random Noise Typically Look?
Nov
29
awarded  Civic Duty
Nov
29
comment How Does Random Noise Typically Look?
Hmm, this looks convincing and the moment map argument is especially nice.