Alphabeta MathHow 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.
FALSE: every 2-narrow graph is 1-narrow
Statement
False claim. Every two-narrow graph is one-narrow.
Facts & Assumptions
Given: The cycle graph .
The graph is two-narrow but not one-narrow (The five-cycle is 2-narrow but not 1-narrow).
Refutation
The example [L1] furnishes a graph that satisfies the hypothesis of the false claim but not its conclusion.
Therefore the implication is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
7 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
- Maria Chudnovsky and Shmuel Safra, The Erdős-Hajnal conjecture for bull-free graphs (standard reference, not scraped)