English

Degrees are Useless in SNORT When Measuring Temperature

Combinatorics 2024-06-05 v1

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 (K1,nK_{1,n} has temperature nn). 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.

Keywords

Cite

@article{arxiv.2406.02107,
  title  = {Degrees are Useless in SNORT When Measuring Temperature},
  author = {Svenja Huntemann and Tomasz Maciosowski},
  journal= {arXiv preprint arXiv:2406.02107},
  year   = {2024}
}
R2 v1 2026-06-28T16:52:37.583Z