subgraph

子图

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

Translation evidence: Literature usage

Meaning in context

A graph H=(W,F) is a subgraph of G=(V,E) when W ⊆ V and F ⊆ E, with every edge of F having its endpoints in W.

图 H=(W,F) 是 G=(V,E) 的子图，意指 W⊆V、F⊆E，且 F 的每条边的端点都属于 W。

Example

A three-vertex path is an ordinary subgraph of a triangle after one edge is omitted.

Usage and distinctions

A subgraph may omit edges between retained vertices; an induced subgraph must retain all of them.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

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

Translation sources

  1. 新疆大学 — 本科课程教学大纲汇编，图论（050762）PDF p.95 / printed p.94，图论课程第一部分，第一章「图与子图」 · Checked 2026-10-14
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