论文标题
飞机的色数至少为5-人为验证的证明
The chromatic number of the plane is at least 5 -- a human-verifiable proof
论文作者
论文摘要
我们提供了一个已知的事实的新证明，即平面的色数至少为5。此证明的主要区别是可以在没有计算机帮助的情况下手动对其进行验证。
We present a new proof of the known fact that the chromatic number of the plane is at least 5. The main difference of this proof is that it can be verified manually without the help of the computer.
