False statementConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge 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.

FALSE: every bull-free graph is perfect

Statement

False claim. Every bull-free graph is perfect.

Facts & Assumptions

Given: The five-cycle $C_{5}$ .

[L1]

The graph $C_{5}$ is bull-free but not perfect (The five-cycle is bull-free but not perfect).

Refutation

technique · direct

1.1

By [L1], the graph $C_{5}$ is already a counterexample to the claim.

2.1

Therefore the claim is false.

step 1.1∎

Depends on

The five-cycle is bull-free but not perfect

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

7 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 (standard reference, not scraped)