Author: José de Jesús García Ruvalcaba
Date: 11:54:13 07/11/04
Go up one level in this thread
On July 11, 2004 at 13:17:58, Uri Blass wrote: >On July 11, 2004 at 13:06:31, José de Jesús García Ruvalcaba wrote: > >>On July 11, 2004 at 12:57:16, Uri Blass wrote: >> >>> >>>Note that it is important to verify before the next round that there is a >>>possible pairing for the next round. >>> >>>Based on my calculation it is possible to do a pairing for the next 2 rounds if >>>the only condition is that programs do not play twice. >>> >> >>As I posted some time ago, for n players (n is even), if you already have done >>n-4 rounds (in this case 14-4=10 rounds) it is posible to do also round n-3 >>(i.e. round 11), you may want to check the archives. >>José. > >I am not sure about this and I suspect that there may be a pairing that it is >impossible to complete. > >This theorem is against my intuition because I can find easily a case when it is >even impossible to do round 8 with 14 players. > >It is not a proof but at least it gives me the impression that the teheorom is >wrong. > >Uri I assume you remember or found my post, there is a reference there which should be easy to find in a big university library. What I state is: every 3-regular graph has a perfect coupling (3-regular means that each vertex has exactly 3 neighbours) This implies that, once you have found pairings for the first n-4 rounds, you can also find them for round n-3. It does not imply that you can find the earlier pairings. José.
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