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Thank you for the very interesting references. It seems that one can not expect a complete answer in the near future, so I would like to accept this one.
FYI, in the paper of Larman and Rogers, the lemma goes like this: "if more than n' (n'=n, n+1, n-1 as you said) triples are chosen from n objects, at least one pair of triples have EXACTLY one element in common"
Either I or Cibulka misunderstand the lemma of Erdös and Sös. The graph in your first paragraph is a Johnson graph J(n,3), it's chromatic number is at most $n$ (Graham and Sloane, 1980). I then checked the paper of Larman and Rogers, it seems that Equation 2.1 in Cibulka's thesis should be about the clique number, not the independence number. Would you please confirm these things?
