DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-11

How 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 $G$ be a finite graph and let $e$ 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 $e$ is a bridge if $G - e$ has more connected components than $G$ . 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 $G$ is disconnected.

Depends on

Used by

An edge of a finite graph is a bridge if and only if it lies on no cycle Lemma

Dependency tree · two levels

9 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

R. Diestel, Graph Theory, 6th ed., Chapter 4, Section 4.2 (standard reference, not scraped)