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 bridge as an edge whose deletion increases the number of connected components
Definition
Let be a finite graph and let be an edge. Using edge deletion from Vertex and edge deletion, edge contraction, graph minors, subdivisions and topological minors and connected components from Connected graphs and connected components defined by the existence of vertex paths, the edge is a bridge if has more connected components than . Component vertex sets partition the graph as in The connected components of a graph partition its vertex set and are its maximal connected subgraphs, so this comparison is unambiguous even when is disconnected.
Depends on
Used by
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 12 results over 8 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
- R. Diestel, Graph Theory, 6th ed., Chapter 4, Section 4.2 (standard reference, not scraped)