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 Bird graph and co-Bird

Definition

The Bird graph is the graph on vertices

${x_{1}, x_{2}, x_{3}, y, z, w}$

with edge set

${x_{1} x_{2}, x_{2} x_{3}, x_{1} x_{3}, x_{1} y, x_{2} z, y w} .$

So ${x_{1}, x_{2}, x_{3}, y, z}$ spans the bull, and $w$ is a new leaf attached to the horn vertex $y$ . The co-Bird graph is the complement of the Bird graph.

Used by

The singleton Bird family has property (*) Corollary
The singleton Bird family is generalized nice Corollary
A six-vertex witness graph makes the Bird criterion explicit Example
The Bird graph and co-Bird by finite adjacency data Example
The Bird theorem reaches an induced bull witness Example
The first co-Bird witness by adjacency Example
The no-E-copy boundary case of the comb partition Example
The second co-Bird witness by adjacency Example
The E-graph and Bird singleton families are leaf-reducible Lemma
The E-graph and the Bird graph are wonderful Lemma
The edge-plus-isolate co-Bird obstruction Lemma
The path-plus-isolate co-Bird obstruction Lemma
A special-vertex co-Bird-free comb admits an E-free structural partition Theorem
The Bird graph has the Erdős-Hajnal property Theorem

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 5 (standard reference, not scraped)