RemarkRemark: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16

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 Erdős–Hajnal conjecture: every fixed forbidden induced graph admits a positive exponent

The Erdős–Hajnal conjecture asserts that every finite graph $H$ has the Erdős–Hajnal property: equivalently, for each $H$ there is an exponent $ϵ (H) > 0$ such that every nonempty $H$ -free graph $G$ satisfies $hom (G) \geq ∣ V (G) ∣^{ϵ (H)}$ (The Erdős–Hajnal property and an Erdős–Hajnal constant for a hereditary graph class, $H$ -free and $F$ -free graphs under the induced-subgraph convention).

Depends on

Used by

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Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 17 results over 7 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources

M. Chudnovsky, The Erdos-Hajnal Conjecture: A Survey, Conjecture 1.1 (standard reference, not scraped)
A. Chernikov, MATH 223M notes, Conjecture 3.1 (standard reference, not scraped)