spanning tree

支撑树

Combinatorics · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A spanning tree of a nonempty finite graph G is a subgraph with the entire vertex set of G that is a tree.

非空有限图 G 的支撑树，是保留 G 全部顶点且本身为树的子图。

Example

Deleting one edge from a four-cycle gives a spanning tree of that cycle.

Usage and distinctions

Spanning refers to vertices, not retention of all edges. A disconnected graph has no spanning tree.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Keller and Trotter — Applied Combinatorics (2016)Section 5.1, spanning subgraph and spanning tree definitions · Checked 2026-10-14

Translation sources

  1. Reinhard Diestel — 图论，第五版，于青林译第二章开篇，印刷p.33，§2.4介绍中的「支撑树」（名称证据） · Checked 2026-10-14
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