Timeline for Hamilton cycle decompositions of the complete graph
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Oct 2, 2010 at 19:11 | comment | added | user9750 | How do i write the number of different Hamiltonian cycles there are in a fully connected graph with n vertices? | |
| Jun 12, 2010 at 6:39 | answer | added | Douglas S. Stones | timeline score: 1 | |
| Jan 24, 2010 at 12:58 | history | edited | Douglas S. Stones | CC BY-SA 2.5 |
added 587 characters in body
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| Jan 24, 2010 at 12:42 | comment | added | Douglas S. Stones | Good point, actually, my count for n=5 above miscount on two fronts. It also overcounts for (12345)^(-1) (13524) as well. | |
| Jan 3, 2010 at 20:34 | answer | added | Harrison Brown | timeline score: 0 | |
| Jan 3, 2010 at 20:06 | answer | added | Emil | timeline score: 3 | |
| Jan 3, 2010 at 17:23 | comment | added | Harrison Brown | Douglas, are you labeling the cycles in the decomposition as well? So (1 2 3 4 5) (1 3 5 2 4) is not the same as (1 3 5 2 4) (1 2 3 4 5)? | |
| Jan 3, 2010 at 14:21 | comment | added | Jason Dyer | Oops, yes, you're right. | |
| Jan 3, 2010 at 14:03 | comment | added | Emil | Jason - that table counts cycles, not decompositions. | |
| Jan 3, 2010 at 13:51 | comment | added | Jason Dyer | There's a table at mathworld.wolfram.com/HamiltonianCycle.html | |
| Jan 3, 2010 at 12:13 | comment | added | Douglas S. Stones | I've tried looking up "Hamilton cycle decompositions" and similar terms in OEIS, Google and MathSciNet without luck. I think the counts for n=3 and n=5 are 1 and 24, respectively (since there are 4! 5-cycles), which is not enough. The count for n=7 seems difficult to compute without coding. But this seems like a very natural question to ask - I'd be surprised if nobody has counted these decompositions before. | |
| Jan 3, 2010 at 10:53 | comment | added | Qiaochu Yuan | Have you tried looking up the first few terms of the sequence in the OEIS? | |
| Jan 3, 2010 at 10:37 | history | asked | Douglas S. Stones | CC BY-SA 2.5 |