A characterization on n-critical economical generalized tic-tac-toe games
✍ Scribed by Xiaoyun Lu
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 419 KB
- Volume
- 110
- Category
- Article
- ISSN
- 0012-365X
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✦ Synopsis
Lu, X., A characterization on n-critical economical generalized tic-tat-toe games, Discrete Mathematics 110 (1992) 197-203.
There is a so called generalized tic-tat-toe game playing on a finite set X with winning sets A,, A,, , A,. Two players, F and 5, 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. Erdos and Selfridge proved that if IAll = iA,/ = t = IA,,, = n and m < 2". ', then the game is a draw. This result is best possible in the sense that once m = 2"-', then there is a family A,, A,,
, A, so that F can win. In this paper we characterize all those sets A,, , A,,-I so that F can win in exactly n moves. We also get similar result in the biased games.