Lu, Xiaoyun A characterization on \(n\)-critical economical generalized tic-tac-toe games. (English) Zbl 0781.90097 Discrete Math. 110, No. 1-3, 197-203 (1992). Summary: There is a so-called generalized tic-tac-toe game playing on a finite set \(X\) with winning sets \(A_ 1,A_ 2,\dots,A_ m\). Two players, \(F\) and \(S\), take in turn a previous untaken vertex of \(X\), with \(F\) going first. The one who takes all the vertices of some winning set first wins the game. P. Erdős and J. L. Selfridge [J. Combinat. Theory, Ser. A 14, 298-301 (1973; Zbl 0293.05004)] proved that if \(| A_ 1|=| A_ 2|=\cdots=| A_ m|= n\) and \(m< 2^{n-1}\), then the game is a draw. This result is best possible in the sense that once \(M=2^{n-1}\), then there is a family \(A_ 1,A_ 2,\dots,A_ m\) so that \(F\) can win. In this paper we characterize all those sets \(A_ 1,\dots,A_{2^{n-1}}\) so that \(F\) can win in exactly \(n\) moves. We also get similar results in the biased games. Cited in 2 Documents MSC: 91A46 Combinatorial games Keywords:generalized tic-tac-toe game Citations:Zbl 0293.05004 PDFBibTeX XMLCite \textit{X. Lu}, Discrete Math. 110, No. 1--3, 197--203 (1992; Zbl 0781.90097) Full Text: DOI References: [1] Beck, J., Remarks on positional games, Acta Math. Acad. Sci. Hungar., 40, 65-71 (1982) · Zbl 0515.90100 [2] Beck, J.; Csirmaz, L., Variations on a game, J. Combin. Theory Ser. A, 33, 297-315 (1982) · Zbl 0505.90100 [3] Erdős, P.; Selfridge, J., On a combinatorial game, J. Combin. Theory, 14, 298-301 (1973) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.