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.
The star-expansion of the four-vertex path contains an induced six-cycle
Example
In the star-expansion of , the vertices induce a six-cycle.
Facts & Assumptions
Given: The star-expansion of with root , teeth , and path vertices .
The only edges using the new vertices are and (The star-expansion of a graph).
Verification
Among the chosen six vertices, the edges are exactly .
The teeth create no further chord, and the path contributes no edge . Hence those six vertices induce a six-cycle.
Depends on
Used by
Nothing in the library uses this result yet.
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, sentence after Theorem 1.9 (standard reference, not scraped)