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.

The graphs $H_{0}, H_{1}, \dots, H_{5}$

Definition

Let $H_{0}$ be the graph on vertices

${w, v_{1}, v_{2}, v_{3}, v_{4}, v_{5}}$

whose edge set is

${w v_{i} : 1 \leq i \leq 5} \cup {v_{1} v_{2}, v_{2} v_{3}, v_{3} v_{4}, v_{4} v_{5}, v_{5} v_{1}} .$

Thus $H_{0}$ is the five-wheel with hub $w$ and rim cycle $v_{1} v_{2} v_{3} v_{4} v_{5} v_{1}$ .

For each $i \in {1, 2, 3, 4, 5}$ , define $H_{i}$ recursively from $H_{i - 1}$ by adjoining a new leaf $v_{i}^{'}$ adjacent only to $v_{i}$ . In particular, $H_{1}$ adds a leaf at $v_{1}$ , and $H_{5}$ adds one leaf at every rim vertex of the five-wheel.

Used by

The graph H₀ has the Erdős-Hajnal property Corollary
H₀ is the five-wheel Example
H₁ and H₅ arise by the stated labelled leaf attachments Example

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Shenwei Huang, Yiao Ju, and Yidong Zhou, Erdős-Hajnal beyond the five-vertex path, Figure 7 (standard reference, not scraped)

The graphs H0,H1,…,H5H0​,H1​,…,H5​

Definition

Used by

Dependency tree · 0 levels

Sources

The graphs $H_{0}, H_{1}, \dots, H_{5}$