Why it matters

Chromatic invariants classify graphs. Understanding shapes graph theory.

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The architecture

chi(G): smallest k for proper coloring.

P(G, k): polynomial in k.

Computed via deletion-contraction.

Chromatic invariantsChromatic numbermin kChromatic polynomialcount coloringsDeletion-contractionP(G) = P(G-e) - P(G/e)Chromatic polynomial has combinatorial + graph structure info
Chromatic.
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How it works end to end

Deletion-contraction: P(G) = P(G-e) - P(G/e).

Recursive computation.

Exponential worst case.