Abstract
The purpose of this paper is to find the general class of graph games with last player losing which may be solved by an analogue ofBouton's [1901] solution. Moreover, it can be shown that this class contains all subtraction games, as well asLasker's [1931] nim and several other games. Games such asKayles andDawson's [1935] game with last player losing are not treated by the method of this paper and are still unsolved.
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