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.
Complete, anticomplete and mixed vertex-set pairs in
Statement
In the path :
- is complete;
- is anticomplete; and
- is mixed.
Facts & Assumptions
Given: with edge set .
Complete means all cross pairs are edges, anticomplete means none are edges, and mixed means some but not all are edges (Edges between disjoint vertex sets; complete, anticomplete, pure and mixed pairs).
The only edges of the path are consecutive pairs (Empty and complete graphs, complete bipartite graphs, and the convention that and have vertices).
Verification
Both and are edges, so is complete.
Neither nor is an edge, so is anticomplete.
The pair is an edge but is not, so is mixed.
These verify the three claimed pair types.
Remarks
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 8 results over 5 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.
Sources
- Valerio Boncompagni, On hereditary graph classes defined by forbidding Truemper configurations (PhD thesis, 2018) (standard reference, not scraped)