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# 🎨 Graph Coloring

Band 4 — The Jupiter transformer. Colour a graph with minimum colours — no adjacent vertex shares a colour.

Vertices: 15 Density: 35%
Ready

### Algorithm: Greedy Sequential Coloring

Order vertices arbitrarily. For each vertex, assign the smallest colour not used by its already-coloured neighbours. Uses at most Δ+1 colours (Δ = max degree). Finding the minimal number of colours (chromatic number) is NP-hard, but greedy gives a usable bound.

### Why This Matters

Graph coloring governs scheduling, frequency allocation, and register allocation. The Jupiter transformer assigns harmonic bands so nothing conflicts — exactly how the 72-band framework avoids frequency collisions.