Abstract

Beineke, Harary, and Ringel discovered a formula for the minimum genus of a torus in which the n-dimensional hypercube graph can be embedded. We give a new proof of the formula by building this surface as a union of certain faces in the hypercube’s 2-skeleton. For odd dimension n, the entire 2-skeleton decomposes into $(n-1)/2$ copies of the surface, and the intersection of any two copies is the hypercube graph.

中文翻译：

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Hypercube属的新观点

摘要

Beineke，Harary和Ringel发现了一个圆环的最小类的公式，其中可以嵌入n维超立方体图。通过将该表面构造为超立方体的2骨架中某些面的并集，我们为公式提供了新的证明。对于奇数维n，整个2骨架分解为$（ñ-\mathrm{1个}）/\mathrm{2个}$ 曲面的两个副本，并且任何两个副本的交点都是超立方体图。