Degrees are Useless in SNORT When Measuring Temperature

Abstract

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 opponents' 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 the temperature in addition can be infinitely larger than the degree of the board being played on. We do so by constructing a family of positions in which the temperature grows twice as fast as the degree of the board.