作者：禅与计算机程序设计艺术
1.简介
In graph theory, planar graphs are those in which all edges can be drawn in a plane such that no point is shared by more than two edges. In other words, the vertices of each edge form segments that do not cross any other segment on the same side as it. Planarity testing is a fundamental problem in computer graphics, pattern recognition, optimization, and computer science. There exist various algorithms for testing whether a given undirected graph is planar or not, but one common approach is to use Kuratowski’s theorem, which states that every connected planar graph has at least three non-intersecting triangles meeting an odd number of times along its boundary. This property allows us to enumerate all possible cut-vertex sets for a given planar graph and test their complements using the triangle inequality theorem, which says that the area of the region inside a polygon must always exceed half the total area outside it.