Alphabeta Math
CorollaryStatement: Literature-sourcedProof: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-31
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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 five-cycle has the Erdős-Hajnal property

Statement

The graph C5 has the Erdős-Hajnal property.

Facts & Assumptions

Given: The graph C5.

[L1]

There exists τ>0 such that every nonempty C5-free graph G satisfies κ(G)≥∣V(G)∣τ (The C5-free graphs satisfy a polynomial kappa bound).

[L2]

For a finite family of graphs, the existence of a positive-power κ-bound is equivalent to the Erdős-Hajnal property (The Erdos-Hajnal property is equivalent to the large-cograph, large-perfect, and kappa formulations).

Proof

technique · direct
1.1

By [L1], the family consisting only of C5 satisfies the κ-formulation of the Erdős-Hajnal property.

L1
2.1

Applying the implication from clause 4 to clause 1 in [L2], we conclude that C5 has the Erdős-Hajnal property.

step 1.1L2∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

25 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