---
tag: PT8MSXSB4Z
kind: concept
name: Spanning
aliases: [spanning-subgraph]
sources:
  - wikipedia: en:325802@r1373839425
    locator: Glossary of graph theory, section S
    note: adopted
    mention: wikipedia://en/325802#KK1K
    sections: [Summary]
inventory: [VZM3QN9JKF]
---

## Summary

A subgraph is spanning when it includes all of the vertices of the given graph. Important cases include [[spanning trees|0FQ5B8S1ZC]] (spanning subgraphs that are trees) and [[perfect matchings|05ZPH8KF9K]] (spanning subgraphs that are matchings). A spanning subgraph may also be called a factor, especially (but not only) when it is regular.