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 strong Erdős–Hajnal property for a hereditary graph class

Definition

Let $C$ be a hereditary class of finite graphs. We say that $C$ has the strong Erdős–Hajnal property if there exists a real constant $ϵ > 0$ such that every graph $G \in C$ with $∣ V (G) ∣ \geq 2$ contains disjoint vertex sets $A, B \subseteq V (G)$ satisfying

$∣ A ∣ \geq ϵ ∣ V (G) ∣, ∣ B ∣ \geq ϵ ∣ V (G) ∣,$

and such that $(A, B)$ is a pure pair in the sense of Edges between disjoint vertex sets; complete, anticomplete, pure and mixed pairs.

Equivalently, every nontrivial graph in the class contains a complete or anticomplete pair whose two sides both have linear size.

Depends on

Used by

Dependency tree · two levels

6 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

Nicolas Bousquet, Aurélie Lagoutte, and Stéphan Thomassé, The Erdős-Hajnal Conjecture for Paths and Antipaths (standard reference, not scraped)