Timeline for Matching on sphere to create cycle with chords
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2013 at 13:21 | vote | accept | Joseph O'Rourke | ||
| Jun 29, 2013 at 13:21 | comment | added | Joseph O'Rourke | Brilliant, Johan! This is essentially the proof that the TSP is noncrossing. You are assuming there exists at least one possibly crossing cycle to get your proof off the ground, but in fact I can modify the argument for arbitrary paths to achieve that. | |
| Jun 29, 2013 at 7:12 | comment | added | Johan Wästlund | Wlodzimierz, I don't understand, what is the difference between cycle and connected cycle? I'm looking at pairings of the points using (possibly crossing) great circle arcs, under the condition that together with the chords they connect the points into a single cycle (rather than several cycles). I'm arguing that among those pairings, the one that minimizes the total length of the arcs is non-crossing (except in the degenerate case illustrated in the OP). | |
| Jun 29, 2013 at 3:30 | comment | added | Włodzimierz Holsztyński | Johan, it's very nice (I even upvoted your answer). But if a cycle is understood as a connected cycle then the question is still open. | |
| Jun 28, 2013 at 22:36 | history | answered | Johan Wästlund | CC BY-SA 3.0 |