eulerpathsandcircuits(編輯修改稿)
2024-11-23 02:58 本頁面
【文章內(nèi)容簡介】 circuit starts at this node, then it must end elsewhere. This is because after we leave the node the first time the node has even degree, and every time we return to the node we must leave it. (On the paired arc.) ? If a node is odd, and the circuit begins else where, then it must end at the node. This is a contradiction, since a circuit must end where it began. Euler Circuit? If a graph has all even degree nodes, then an Euler Circuit exists. ? Algorithm: ? Step One: Randomly move from node to node, until stuck. Since all nodes had even degree, the circuit must have stopped at its starting point. (It is a circuit.) ? Step Two: If any of the arcs have not been included in our circuit, find an arc that touches our partial circuit, and add in a new circuit. ? Each time we add a new circuit, we have included more nodes. ? Since there are only a finite numbe
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