DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16

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.

Graph edit distance and being $ϵ$ -far from an induced-hereditary property

Definition

For two finite simple graphs $G, G^{'}$ on the same vertex set, their edit distance is $dist (G, G^{'}) : = ∣ E (G) △ E (G^{'}) ∣,$ the number of unordered vertex pairs whose adjacency must be changed to turn $G$ into $G^{'}$ . If $G$ has order $n$ and $P$ is a hereditary graph property (Hereditary graph classes), then $G$ is $ϵ$ -far from $P$ when $dist (G, G^{'}) \geq ϵ n^{2}$ for every graph $G^{'} \in P$ on $V (G)$ . Edits may delete edges or add nonedges.

Depends on

Used by

Induced graph removal lemma for a fixed graph Theorem

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 13 results over 10 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

D. Conlon and J. Fox, Graph removal lemmas, sec. 2.3 (standard reference, not scraped)

Graph edit distance and being ϵϵ-far from an induced-hereditary property