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.
A connected graph with two distinct spanning trees
Statement
The triangle is connected and has three distinct spanning trees, obtained by deleting any one edge.
Facts & Assumptions
Given: The cycle graph .
is connected and has three edges (Empty and complete graphs, complete bipartite graphs, and the convention that and have vertices).
A spanning tree is a connected acyclic spanning subgraph (Spanning trees of a graph).
A finite graph is connected if and only if it has a spanning tree (A finite graph is connected if and only if it has a spanning tree).
Verification
Deleting any edge of leaves a two-edge path on all three vertices, so each result is a spanning tree.
The three deleted edges are different, so the three resulting edge sets are distinct. In particular, this connected graph has at least two spanning trees.
Depends on
Used by
- Every edge of a connected graph lies in every spanning tree False statement
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 18 results over 10 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
- Reinhard Diestel, Graph Theory, Preview Chapter 1 (standard reference, not scraped)