Timeline for When is a triangulation of sphere two-colorable?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 24, 2021 at 6:47 | history | became hot network question | |||
| Jun 24, 2021 at 3:23 | vote | accept | Hailong Dao | ||
| Jun 24, 2021 at 0:15 | history | edited | Tony Huynh |
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| Jun 23, 2021 at 23:59 | answer | added | Tony Huynh | timeline score: 11 | |
| Jun 23, 2021 at 23:59 | comment | added | Sam Hopkins | @HailongDao: consider the planar dual graph. The condition of the primal graph having each vertex of even degree is the same as each face of the dual graph having an even number of edges. It is a small exercise to show that for planar graphs this implies that every cycle has even length, which is well-known to be equivalent to the graph being bipartite (i.e., vertex 2-colorable). | |
| Jun 23, 2021 at 23:42 | comment | added | Hailong Dao | @FedorPetrov: that sounds reasonable. Is there a reference, and if not, would you mind giving a full answer? Thanks. | |
| Jun 23, 2021 at 23:05 | comment | added | Fedor Petrov | Each vertex should have even degree (this is necessary and sufficient for 2-dimensional sphere.) | |
| Jun 23, 2021 at 22:53 | comment | added | Hailong Dao | Yes, but one can formulate the question in higher dimensions. | |
| Jun 23, 2021 at 22:51 | comment | added | Sam Hopkins | Everything is $2$-dimensional here? | |
| Jun 23, 2021 at 22:46 | history | asked | Hailong Dao | CC BY-SA 4.0 |