Snort how hot can a vertex be?
Blue (Left) and Red (Right) take turns colouring a vertex of the graph. You may not colour a vertex next to one of the other colour. Whoever cannot move loses. A coloured vertex reserves its neighbours for its own side (they are drawn tinted), so a move is worth more the more it reserves: the temperature measures how urgent it is to move first. It was conjectured to be at most the largest degree; the presets include the counterexamples. With hints on, every legal move is marked ✓ (keeps the win) or ✗.
value of the position
components
How the values are computed
A coloured vertex leaves the game and tints its uncoloured neighbours with its colour; a vertex tinted both ways is dead, and an edge between two vertices tinted alike no longer matters. What is left falls apart into components, the game is their sum, and each component is valued once from its options and reduced to canonical form (trees are keyed up to isomorphism). The thermograph is built from the canonical form: the left wall from Left's options taxed by t, the right wall from Right's, and the temperature is where they meet.
Checked against the literature
The repository recomputes, from the arXiv TeX sources, Table 1, Theorem 3.7 and every step of its proof in S. Huntemann and T. Maciosowski, Degrees are useless in Snort when measuring temperature (2024); the path and 2×n tables of Huntemann, Nowakowski and dos Santos, Bounding game temperature using confusion intervals (TCS 2021), including two columns left commented out in the source; and the first-player wins on triangular grids of Gauthier and Huntemann (2024). Conjecture 5.1 (t ≤ deg + deg₂/2) is tested on every tree and every small connected graph.