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 middle edge of is a maximal matching but the two end edges form a larger matching
Counterexample
Let have consecutive vertices and let . Then is maximal but not maximum: is a matching of size two.
Facts & Assumptions
Given: The path and its middle-edge matching .
A matching is maximum exactly when it has no augmenting path (Berge's theorem: a matching is maximum if and only if it has no augmenting path).
Verification
Verification technique: direct.
The two remaining edges and each meet , so neither can be added to ; hence is maximal.
The path is -augmenting, and [L1] therefore also shows that is not maximum.
Independently, is a disjoint two-edge matching, so the maximal and maximum notions differ in this finite path.
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: 15 results over 7 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.