论文标题
将K3,3和K5嵌入双曲线
Embedding K3,3 and K5 on the Double Torus
论文作者
论文摘要
kuratowski图$ k_ {3,3} $和$ k_5 $表征平面。以前使用Burnside的引理及其自动形态组来计算这两个图在定向表面上的不同的2细胞嵌入，而无需实际构造嵌入。我们使用建设性方法在双圆环上获得这些图形的所有2细胞嵌入。这表明，在双圆环上有$ k_ {3,3} $，14个定向的不可定向的2细胞嵌入$ k_ {3,3} $，14个不可方向的2细胞嵌入$ k_5 $的嵌入，这明确确认了枚举结果。结果，提出了双带的几种新的多边形表示。
The Kuratowski graphs $K_{3,3}$ and $K_5$ characterize planarity. Counting distinct 2-cell embeddings of these two graphs on orientable surfaces was previously done by using Burnside's Lemma and their automorphism groups, without actually constructing the embeddings. We obtain all 2-cell embeddings of these graphs on the double torus, using a constructive approach. This shows that there is a unique non-orientable 2-cell embedding of $K_{3,3}$, 14 orientable and 17 non-orientable 2-cell embeddings of $K_5$ on the double torus, which explicitly confirms the enumerative results. As a consequence, several new polygonal representations of the double torus are presented.
