V2EX topological minor

Topological Minor

释义 Definition

(图论)拓扑小图 / 拓扑次图:若图 \(G\) 含有某个图 \(H\) 的细分(subdivision)作为子图,则称 \(H\) 是 \(G\) 的 topological minor。等价地,可以通过对 \(G\)删点、删边,并把度为 2 的顶点“抑制/平滑”(suppress)(把两条边合并成一条)来得到 \(H\)。
(注:这里的 minor 是图论术语“(图)小图”,不同于日常英语“较小的/次要的”。)

发音 Pronunciation

/tpldkl manr/

例句 Examples

A triangle is a topological minor of many larger graphs.
三角形是许多更大图的一个拓扑小图。

The theorem states that excluding a fixed topological minor imposes strong structural constraints on the graph.
该定理指出:排除某个固定的拓扑小图会对图的结构施加很强的限制。

词源 Etymology

Topological 源自 topology(拓扑学),表示与“形状在连续变形下保持的性质”相关;在图论里,这种“连续变形”的直观对应到把边拉长并插入度为 2 的顶点(细分),但不改变图的“连接方式”。Minor 在图论中指通过允许的简化操作得到的“更小的图”。因此 topological minor 强调的是:通过细分/抑制度为 2 顶点

相关词 Related Words

文学与著作中的用例 Literary Works

  • Reinhard Diestel, Graph Theory(多处以“subdivision / topological minor”讨论图的细分与包含关系)
  • Douglas B. West, Introduction to Graph Theory(在平面图与禁用结构等主题中提及相关概念)
  • Neil Robertson & Paul Seymour, “Graph Minors” 系列论文(与小图理论相关的经典文献中常对比 minortopological minor
  • Bojan Mohar & Carsten Thomassen, Graphs on Surfaces(在曲面上的嵌入与结构理论语境中涉及 topological minor
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