ExampleConstruction: AI-generatedVerification: Not suppliedSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-27

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.

A three-tooth comb

Example

Let $G$ be a graph with six pairwise distinct vertices $a_{1}, a_{2}, a_{3}, b_{1}, b_{2}, b_{3}$ . Put

$B_{1} = {b_{1}}, B_{2} = {b_{2}}, B_{3} = {b_{3}} .$

If $a_{i}$ is adjacent to $b_{i}$ and to no other $b_{j}$ , then

$((a_{1}, B_{1}), (a_{2}, B_{2}), (a_{3}, B_{3}))$

is a $(3, 1)$ -comb.

Depends on

Combs in a graph

Used by

Nothing in the library uses this result yet.

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

Shenwei Huang, Yiao Ju, and Yidong Zhou, Erdős-Hajnal beyond the five-vertex path (standard reference, not scraped)