DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-01

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.

Leaf-reducible finite graph families

Definition

Let $F$ be a finite family of finite graphs. We say that $F$ is leaf-reducible if there exist a graph $H \in F$ and a leaf $v \in V (H)$ such that the modified family

$F^{'} : = {H ∖ {v}} \cup (F ∖ {H})$

has the Erdős-Hajnal property in the family sense (The Erdős–Hajnal property and an Erdős–Hajnal constant for a hereditary graph class, $H$ -free and $F$ -free graphs under the induced-subgraph convention).

Thus a leaf-reducible family is one for which deleting one leaf from one member produces a new forbidden family already known to have the Erdős-Hajnal property.

Depends on

Used by

Dependency tree · two levels

12 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, Section 2.2 (standard reference, not scraped)