Computing & AI · the experiment
Free up a colour
A map, four colours, chains whose colours you swap. Four questions, from beginner to expert, on how to find those colours fast.
1 · Say what the paper adds
Beginner
What does this paper add to the four colour theorem?
2 · Work out the chance of a repair
A random Kempe change: pick one of the three possible pairings of the four colours, then toss a coin for each chain to decide whether to swap it. It helps a ring if it picks the right pairing and the right toss for every chain touching the ring.
Intermediate
A ring is touched by 4 chains. What is the minimum chance that a random change helps it?
3 · Free up a colour for v
A vertex v has four neighbours, v0, v1, v2 and v3 in order around it, coloured 1, 2, 3 and 4. No colour is left for v. The Kempe chain starting at v0 in colours 1 and 3 reaches v2.
Expert
Which swap frees a colour for v?
4 · Decide a chain
Two live rings touch the same chain K, still undecided. Ring A touches 2 undecided chains, K included, and wants K swapped. Ring B touches 3, K included, and wants K kept.
Expert
What does the algorithm choose for K?
Colour freed
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