DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-05

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

The three-colourability decision problem

Definition

Let $G = (V, E)$ be a finite simple graph. A proper three-colouring of $G$ is a map $κ : V \to {0, 1, 2}$ such that $κ (u) \neq κ (v) whenever {u, v} \in E .$

The decision problem $3$ -COLORABILITY asks, given $G$ , whether such a proper three-colouring exists.

Depends on

Used by

Dependency tree · two levels

3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

John E. Savage, Models of Computation, Chapter 8 (standard reference, not scraped)