On sums of graph games with last player losing

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.