DefinitionDefinition: AI-adaptedProof: Not applicableSession-authored (Fable 5 assisted)audited 2026-08-01

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 complement of a graph class

Definition

For a graph class $\mathcal C$ , its complement class is

$\overline{\mathcal C}:=\{G:\overline G\in\mathcal C\}.$

It consists exactly of those graphs whose complements belong to $\mathcal C$ . If $\mathcal C$ is isomorphism-closed, this is equivalently the isomorphism-closed class of complements of members of $\mathcal C$ (Graph isomorphisms, automorphisms and graph complements). The notation does not mean set-theoretic complement inside the class of all graphs.

When $\mathcal C$ is isomorphism-closed, so is $\overline{\mathcal C}$ , because an isomorphism of graphs induces an isomorphism of their complements.

Depends on

Used by

Complementation preserves hereditary classes and complements their minimal forbidden bases Theorem

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 9 results over 7 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

ISGCI, Self-complementary classes (standard reference, not scraped)