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引用次数: 7
摘要
摘要研究几何图论中的一个问题:在欧几里得三维空间中，在相同体积的基本域上的所有图中，确定最小长度的三周期图。最小化器是所谓的带有商的网络，四个顶点上的完全图$$K_4$$ K 4。为了比较，我们考虑一个竞争的拓扑类，同样在四个顶点上有一个商，并确定最小化网络。
Abstract We study a problem of geometric graph theory: We determine the triply periodic graph in Euclidean 3-space which minimizes length among all graphs spanning a fundamental domain with the same volume. The minimizer is the so-called network with quotient the complete graph on four vertices $$K_4$$ K4 . For comparison we consider a competing topological class, also with a quotient on four vertices, and determine the minimizing networks.
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