Timeline for Matching on sphere to create cycle with chords
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 20, 2017 at 10:37 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Image links broken; now fixed.
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jun 29, 2013 at 13:21 | vote | accept | Joseph O'Rourke | ||
| Jun 29, 2013 at 3:37 | comment | added | Włodzimierz Holsztyński | One may pose a related question about a finite subset of the projective plane and the arcs of the straight lines--there are just simple points, no notion of any antipodal points. The questions are essentially different but at least they are similar, and the projective version has simpler formulation I'd think (a single projective point is something of a substitute, not exactly, of an antipodal pair). | |
| Jun 28, 2013 at 23:48 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
added 47 characters in body
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| Jun 28, 2013 at 22:36 | answer | added | Johan Wästlund | timeline score: 4 | |
| Jun 28, 2013 at 18:03 | comment | added | Johan Wästlund | Answering my own question: When $n\geq 2$, the convex hull is spanned by at least 3 points, so we can find two of them that are adjacent and of different color, say red and green. After pairing them up, we solve the subproblem of the remaining $2n-2$ points under red-green color blindness (treating the other red and green points as having the same color). | |
| Jun 28, 2013 at 14:41 | comment | added | Joseph O'Rourke | That's a wonderfully clarifying reformulation of the essence of the discrete geometry question at the heart of this! | |
| Jun 28, 2013 at 14:04 | comment | added | Johan Wästlund | Is it relevant/necessary that the points are on a sphere and chords are connecting nearly antipodal points? What if there are $2n$ points in "general position" in the plane and they are colored by $n$ colors, 2 points of each color. Can we always find a perfect matching of non-crossing line segments such that a walk that alternates between following a line segment and jumping to the other point of the same color will connect the points to a single cycle? | |
| Jun 28, 2013 at 11:48 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |