DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-28

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 bull graph

Definition

The bull graph is the finite simple graph on vertices ${x_{1}, x_{2}, x_{3}, y, z}$ with edge set

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

Thus ${x_{1}, x_{2}, x_{3}}$ spans a triangle, and $y$ and $z$ are pendant vertices attached to two distinct vertices of that triangle.

Depends on

A finite simple graph is a finite vertex set together with a set of two-element vertex subsets

Used by

The five-cycle is bull-free but not perfect Counterexample
A bull-free graph Definition
The bull graph is self-complementary Example
A graph is bull-free if and only if its complement is bull-free Proposition

Dependency tree · two levels

2 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

Maria Chudnovsky and Shmuel Safra, The Erdős-Hajnal conjecture for bull-free graphs, Section 1 (standard reference, not scraped)