DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-01

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 $E$ -graph and co- $E$

Definition

The $E$ -graph is the graph on vertices

${p_{1}, p_{2}, p_{3}, p_{4}, p_{5}, q}$

with edge set

${p_{1} p_{2}, p_{2} p_{3}, p_{3} p_{4}, p_{4} p_{5}, p_{3} q} .$

Thus $p_{1} p_{2} p_{3} p_{4} p_{5}$ is a five-vertex path and $q$ is a leaf attached to its middle vertex $p_{3}$ . The co- $E$ graph is the complement of this graph.

Used by

The E-graph and co-E by finite adjacency data Example

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Shenwei Huang, Yiao Ju, and Yidong Zhou, Erdős-Hajnal beyond the five-vertex path, Figure 4 (standard reference, not scraped)

The EE-graph and co-EE

Definition

Used by

Dependency tree · 0 levels

Sources

The $E$ -graph and co- $E$