DefinitionDefinition: Literature-sourcedProof: Not applicablejudge 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 · two levels

5 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

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