翻译成英语：我们假设最长圈的长度为偶数即n为偶数。不失一般性我们考虑x2v2那么x2至少和v4v6v8vn之间有边否则将违背k1

We assume that the length of the longest loop is even, that is, n is even. Without loss of generality, we consider x2v2. Then x2 is connected to at least v4, v6, v8,..., vn, otherwise it will violate k1.