Timeline for Curves in the plane and their number of holes
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 1, 2022 at 13:36 | vote | accept | ray | ||
| Nov 1, 2022 at 13:36 | |||||
| Oct 27, 2022 at 6:27 | comment | added | Wlod AA | @ray, Alexandre's argument in the ultimate detail: Let $K$ be the set of all pairs vertex-edge. Then $$ 4\cdot v\ = \ |K|\ =\ 2\cdot e\ $$ hence $\ e=2\cdot v$. | |
| Oct 26, 2022 at 19:24 | comment | added | ray | I don't understand what you want to say here, but this seems to come from the degree sum formula $\sum_{v\in V} deg(v) =2 e$ | |
| Oct 26, 2022 at 18:42 | comment | added | Alexandre Eremenko | From each vertex 4 ends of the edges stick. Each edge has 2 ends. Therefore the number of edges is 2v. | |
| Oct 26, 2022 at 15:10 | comment | added | ray | Great idea. Could you please elaborate a bit on the e=4v/2 identity? Thanks. | |
| Oct 26, 2022 at 14:28 | history | answered | Alexandre Eremenko | CC BY-SA 4.0 |