extremal graph theory

极值图论

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

Translation evidence: Literature usage

Meaning in context

Extremal graph theory studies optimal values of graph parameters under structural restrictions, such as the maximum edge count of an n-vertex graph avoiding a fixed subgraph.

极值图论研究图在给定结构限制下某个参数的最优值，例如固定顶点数并禁含指定子图时的最大边数。

Example

Among seven-vertex triangle-free graphs, the largest edge count is 12, attained by K3,4K_{3,4}.

Usage and distinctions

Specify the optimized parameter and whether forbidden copies are ordinary or induced; those choices define different problems.

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Definition sources

  1. Yufei Zhao — Graph Theory and Additive Combinatorics, author manuscriptChapter 1, Definition 1.0.2 and Question 1.0.3 · Checked 2026-10-14

Translation sources

  1. Reinhard Diestel — 图论，第五版，官方中文目录目录，第七章「极值图论」（名称证据） · Checked 2026-10-14
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