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%I #9 Nov 14 2019 17:53:08
%S 0,1,2,4,8,14,28
%N Least number m such that every tournament with at least m nodes contains the acyclic n-node tournament.
%C A Ramsey-like number but defined for tournaments (i.e., directed graphs in which each node-pair is joined by exactly one arc) rather than undirected graphs.
%C It is not hard to show that a(n) always exists and a(n) is nondecreasing.
%C The lower bounds a(4)>=8 and a(5)>=14 and a(6)>=28 arise from the cyclic tournaments with offsets 1,2,4 mod 7; the same is true of offsets 1,3,9,2,6,5 mod 13 and the "QRgraph" in GF(3^3) with 27 vertices.
%C The following lower bounds a(n)>=P+1 arise from QRgraph(P) where P is prime and P=3 (mod 4): a(8)>=48, a(9)>=84, a(10)>=108, a(12)>=200, a(13)>=272.
%C This is almost certainly different from the other sequences currently in the OEIS which begin 1,2,4,8,14,28.
%D K. B. Reid, Tournaments, in Handbook of Graph Theory; see p. 167.
%H W. D. Smith, <a href="http://rangevoting.org/PuzzDG.html">Partial Answer to Puzzle #21: Getting rid of cycles in directed graphs</a>
%H Yahoo Groups, <a href="http://groups.yahoo.com/group/RangeVoting/">Range Voting</a>
%H Range Voting Yahoo Group, <a href="/A003141/a003141.txt">Introduction</a>. [Cached copy]
%H RangeVoting.org, <a href="https://rangevoting.org/">Group Website</a>.
%H W. D. Smith, <a href="http://rangevoting.org/PuzzRamsey.html">Survey on directed graph Ramsey Numbers</a>.
%Y Cf. A122027, A003141.
%K nonn
%O 0,3
%A _Warren D. Smith_, Sep 11 2006
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