Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedSession-authored (Fable 5 assisted)precheck passjudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16
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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.

[L1]

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).

[L2]

A graph class is hereditary when it is closed under isomorphism and induced subgraphs (Hereditary graph classes).

Refutation

technique · direct
1.1

The class of all finite graphs is closed under isomorphism and induced subgraphs, so it is hereditary by [L2].

L2
2.1

This hereditary class fails the Erdős–Hajnal property by [L1], contradicting the asserted universal claim.

step 1.1L1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 25 results over 6 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