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.

Anticonnected graphs and anticonnected components

Definition

A graph $G$ is anticonnected, or co-connected, when its complement $\overline G$ is connected (Connected graphs and connected components defined by the existence of vertex paths, Graph isomorphisms, automorphisms and graph complements).

An anticonnected component, or anticomponent, of $G$ is a vertex set $A\subseteq V(G)$ that is the vertex set of a connected component of $\overline G$ . Equivalently, $G[A]$ is anticonnected and $A$ is inclusion-maximal with that property (Subgraphs, induced subgraphs and spanning subgraphs).

Under the library convention, the null graph is not anticonnected, while a one-vertex graph is anticonnected.

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 12 results over 8 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

Valerio Boncompagni, On hereditary graph classes defined by forbidding Truemper configurations (PhD thesis, 2018) (standard reference, not scraped)