two-color clique Ramsey number

拉姆齐数

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

Other names / variants: Ramsey number · Ramsey数

Translation evidence: Literature usage

Meaning in context

For positive integers s,t, R(s,t) is the least positive N such that every red-blue edge coloring of K_N has a red K_s or a blue K_t.

对正整数 s、t，R(s,t) 是使 K_N 的每一种红蓝边着色都包含红色 K_s 或蓝色 K_t 的最小正整数 N。

Example

R(3,3)=6R(3,3)=6; coloring a five-cycle red and the other edges of K5K_5 blue avoids both triangles.

Usage and distinctions

These are edge colors, not proper vertex colors. A one-vertex clique is monochromatic vacuously, giving R(1,t)=1.

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Definition sources

  1. Joy Morris — Combinatorics, version 2.1.1Section 14.2, Definition 14.2.2, Example 14.2.3 and Proposition 14.2.4 · Checked 2026-10-14

Translation sources

  1. 中国科学技术大学数学科学学院 — 马杰教授团队在拉姆齐数下界研究中取得突破性进展文章标题和正文首段「拉姆齐数」；仅作为名称证据 · Checked 2026-10-14
  2. Reinhard Diestel — 图论，第五版，官方中文目录目录，§9.2「Ramsey数」（混合文字别名证据） · Checked 2026-10-14
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