DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-27

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 pattern graph of a pure blockade

Definition

Let $B = (B_{1}, \dots, B_{t})$ be a pure blockade in a graph $G$ . Its pattern graph is the graph $P (B)$ with vertex set $[t]$ in which $i$ and $j$ are adjacent exactly when $B_{i}$ is complete to $B_{j}$ .

Because the blockade is pure, every unordered pair of distinct blocks is either complete or anticomplete, so this graph is well defined. A pattern graph is called $P_{4}$ -free when it contains no induced four-vertex path.

Depends on

Complete, anticomplete, pure, weakly sparse, and $x$-sparse blockades

Used by

Dependency tree · two levels

4 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

Maria Chudnovsky, Alex Scott, Paul Seymour, and Sophie Spirkl, Erdős-Hajnal for graphs with no 5-hole (standard reference, not scraped)