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单词 Planar Separator Theorem
释义

Planar Separator Theorem

英语百科

Planar separator theorem

A planar separator for a grid graph.
A polyhedron formed by replacing each of the faces of an icosahedron by a mesh of 100 triangles, an example of the lower bound construction of Djidjev (1982).
An intersection graph of disks, with at most k = 5 disks covering any point of the plane.

In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split into smaller pieces by removing a small number of vertices. Specifically, the removal of O(√n) vertices from an n-vertex graph (where the O invokes big O notation) can partition the graph into disjoint subgraphs each of which has at most 2n/3 vertices.

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更新时间:2025/6/23 5:02:43