Timeline for Given a graph embedded on a torus, how many edges are necessary for noncontractible loops to be long?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Oct 22, 2010 at 11:41 | history | edited | Graham | CC BY-SA 2.5 |
Corrected error
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| Oct 20, 2010 at 16:29 | answer | added | Tony Huynh | timeline score: 3 | |
| Oct 20, 2010 at 10:47 | history | edited | Graham | CC BY-SA 2.5 |
Added simpler problem statement
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| Oct 20, 2010 at 8:16 | answer | added | Fiktor | timeline score: 2 | |
| Oct 20, 2010 at 1:41 | comment | added | Graham | The last comment should say edge-width n - apologies. | |
| Oct 20, 2010 at 1:40 | comment | added | Graham | I would consider this graph to have lots of dual loops of length 1, in the same way as an edge from a vertex to itelf which wraps around the torus could form a (primal) loop of length 1. Thanks for pointing me to the correct terminology - yes, by condition (2), I mean that the graph has face-width n. (And condition (1), that the graph has edge-width 1.) | |
| Oct 20, 2010 at 0:56 | comment | added | Tony Huynh | If I take two cycles of length $n$ glued together at a vertex, and embed them on the torus as two non-homotopic non-contractible curves, do I satisfy the conditions? It seems like (1) and (3) are satisfied, and probably (2) as well since the dual graph only has one vertex. Maybe you want the minimum number of edges of a graph of face-width (representativity) $n$? | |
| Oct 19, 2010 at 14:55 | history | asked | Graham | CC BY-SA 2.5 |