DefinitionDefinition: AI-adaptedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-28

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.

Co-leaves of a finite graph

Definition

Let $G$ be a finite graph and let $v \in V (G)$ . We say that $v$ is a co-leaf of $G$ if $v$ is a leaf of the complement graph $\overline{G}$ .

Equivalently, $v$ is adjacent in $G$ to every vertex of $G$ except one. In degree language,

$\deg_{G} (v) = ∣ V (G) ∣ - 2.$

Thus a co-leaf is the complement-theoretic analogue of an ordinary leaf.

Depends on

Used by

A co-leaf of P₅ is exactly a leaf of P₅ Example

Dependency tree · two levels

8 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

Shenwei Huang, Yiao Ju, and Yidong Zhou, Erdős-Hajnal beyond the five-vertex path, Theorem 1.7 (standard reference, not scraped)