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Embedding Graphs in Cylinder and Torus Books

机译:在圆柱体和圆环书中嵌入图形

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In the classical book embedding problem a k-book is defined to be a line L in 3-space (the spine) together with k half-planes (the pages) joined together at L. We introduce two variations on the classical book in which edges are allowed to wrap in either one or two directions. The first is a cylindrical book where the spine is a line L in 3-space and the pages are nested cylindrical shells joined together at L. The second is a torus book where the spine is the inner equator of a torus and the pages are nested torus shells joined together at this equator. We give optimal edge bounds for embeddings of finite simple graphs in cylinder and torus books and give best-possible embeddings of K_n in torus books. We also compare both books with the classical book.
机译:在经典书的嵌入问题中,将一本k-书定义为在3空间(书脊)中的线L与在L处连接在一起的k个半平面(书页)。我们在经典书中介绍了两种变体,其中允许沿一个或两个方向包裹边缘。第一本是圆柱书,其中书脊是3空间中的L线,页面是嵌套的圆柱壳,在L处连接在一起。第二本是圆环书,其中书脊是圆环的内部赤道,并且书页被嵌套环形壳在此赤道处连接在一起。我们给出了圆柱和圆环书中有限简单图的嵌入的最佳边边界,并给出了圆环书中K_n的最佳可能嵌入。我们还将这两本书与古典书进行了比较。

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