Degrees are useless in Snort when measuring temperature

Snort is a two-player game played on a simple graph in which players alternately colour a vertex such that they do not colour adjacent to their opponent’s vertex. In combinatorial game theory, the temperature of a position is a measure of the urgency of moving first. It is known that the temperature of Snort in general is infinite ( K 1 , n has temperature n ). We show that for all constants c there is a game of Snort for which the difference between the temperature and the maximum degree of the board is at least c . We do so by constructing a family of positions in which the temperature grows twice as fast as the maximum degree of the board.