运筹学 网络最优化问题之欧拉定理是什么
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Euler's Theorem 1
If a graph has any vertex of odd degree then it cannot have an euler circuit.
如果一个图有奇点，则该图不包含欧拉圈。
If a graph is connected and every vertex is of even degree, then it at least has one euler circuit.
如果一个连通图每个点都是偶点，则该图至少有一个欧拉圈。
Euler's Theorem 2
If a graph has more than two vertices of odd degree then it cannot have an euler path.
如果一个图的奇点数大于2，则它不包含欧拉链。
If a graph is connected and has just two vertices of odd degree, then it at least has one euler path. Any such path must start at one of the odd-vertices and end at the other odd vertex.
如果一个连通图恰有两个奇点，它至少包含一个欧拉链，这样的欧拉链一定始于一个奇点，结束于另一奇点。
