DefinitionDefinition: AI-adaptedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07

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 E overlap blockade and mixed quotient sequence

Definition

Fix a comb block $B_{i}$ with nonempty $E$ overlap support $X_{i}$ . By E overlap classes form an anticonnected partition, its overlap classes are nonempty anticonnected sets partitioning $X_{i}$ . Fix an enumeration of the finite set $B_{i}$ , and order the classes by their least enumerated vertex to obtain $L^{1}$ . Define recursively $L^{s + 1} = L^{s} / M$ for $s \geq 1$ , using The quotient blockade obtained from mixed-block reachability and its least-member ordering. Thus one replaces each mixed-reachability class of blocks by its union. This construction is used only when $X_{i} \neq \emptyset$ .

Depends on

Used by

Dependency tree · two levels

7 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

Huang–Ju–Zhou, Erdős–Hajnal beyond the five-vertex path, §6.2, Lemma 6.5, quotient construction (standard reference, not scraped)