Alphabeta MathHow 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.
Every hereditary graph class has the Erdős–Hajnal property
Statement
Every hereditary graph class has the Erdős–Hajnal property.
Facts & Assumptions
Given: The asserted universal claim.
The class of all finite graphs does not have the Erdős–Hajnal property (The hereditary class of all finite graphs does not have the Erdős–Hajnal property).
A graph class is hereditary when it is closed under isomorphism and induced subgraphs (Hereditary graph classes).
Refutation
The class of all finite graphs is closed under isomorphism and induced subgraphs, so it is hereditary by [L2].
This hereditary class fails the Erdős–Hajnal property by [L1], contradicting the asserted universal claim.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
8 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
- A. Chernikov, MATH 223M notes, sec. 3.1 (standard reference, not scraped)