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.

A blockade-rainbow induced copy

Definition

Let $G$ be a graph and let $B = (B_{1}, \dots, B_{t})$ be a blockade in $G$ . An induced subgraph $H$ of $G$ is $B$ -rainbow when

$V (H) \subseteq V (B) and ∣ B_{i} \cap V (H) ∣ \leq 1 for every i \in [t] .$

Equivalently, $H$ lies inside the support of the blockade and each block contributes at most one vertex to it (Blockades, their length, their width, and their support, Subgraphs, induced subgraphs and spanning subgraphs).

We say that a graph $F$ has a $B$ -rainbow induced copy in $G$ when $G$ contains an induced copy of $F$ whose image is $B$ -rainbow (Induced embeddings and induced copies of a graph).

Depends on

Used by

A four-block blockade-rainbow copy of P₄ Example

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

Maria Chudnovsky, Alex Scott, Paul Seymour, and Sophie Spirkl, Erdos-Hajnal for graphs with no 5-hole, Section 6 (standard reference, not scraped)