“可约简的”
用英语怎么说？

Kempe originally attempted to prove the theorem by assuming its opposite: that an uncolorable map existed. He simplified the map into a network known as a planar graph, where countries became points and borders became lines. Relying on mathematical properties discovered by Euler, Kempe argued that every graph contains an unavoidable set of configurations. He believed that each configuration was reducible, meaning that if you removed it, colored the rest, and added it back, you could swap colors without needing a fifth color. However, an error was discovered eleven years later. Kempe's approach failed because one configuration could not be easily reduced, revealing that a complete proof would require verifying thousands of distinct cases.

肯普最初试图通过假设相反的情况来证明该定理：即存在一张无法着色的地图。他将地图简化为一种被称为平面图的网络，其中各个国家变成顶点，边界变成边。依据欧拉发现的数学性质，肯普论证了每个图都包含一个不可避免集构型。他认为每个构型都是可约简的，这意味着如果你将其移除、为其余部分着色后再放回，就可以调换颜色而不需要第五种颜色。然而，11年后有人发现了一个错误。肯普的方法失败了，因为有一种构型无法轻易约简，这表明完整的证明需要核验数千种不同的情况。