DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-02

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.

Alternating and augmenting paths relative to a matching

Definition

Let $M$ be a matching of $G$ . A path is $M$ -alternating if consecutive edges alternately lie outside and inside $M$ . It is $M$ -augmenting if it is $M$ -alternating, its first and last edges lie outside $M$ , and its two endpoints are $M$ -exposed. Thus an augmenting path has odd length, including the possible one-edge path between two exposed vertices.

Depends on

Used by

Dependency tree · two levels

5 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

M. Goemans, Lecture notes on bipartite matching (standard reference, not scraped)