论文标题
不可定向表面的短拓扑分解
Short Topological Decompositions of Non-Orientable Surfaces
论文作者
论文摘要
在本文中，我们研究了不可定向表面的简短拓扑分解，并提供了计算它们的算法。我们的主要结果是一种多项式时间算法，对于嵌入在不可取向表面中的任何图，都可以计算出规范的不可方向的环路系统，以便从规范系统中的任何环中的任何环在最多30点相交图形的任何边缘。在可定向的情况下，存在如此短的循环系统，在不可定向的情况下是一个众所周知的。我们的证明技术将Schaefer-štefankovič最近的工作与来自计算生物学的想法相结合，特别是来自Hannenhalli-Pevzner的签名逆转距离算法。短规范性不可方向的环路的存在证实了在两个可嵌入图的交叉数字上的negami猜想的特殊情况。我们还提供了一个校正，即对negami界定两个不可取向图嵌入的连接交叉数的论点。
In this article, we investigate short topological decompositions of non-orientable surfaces and provide algorithms to compute them. Our main result is a polynomial-time algorithm that for any graph embedded in a non-orientable surface computes a canonical non-orientable system of loops so that any loop from the canonical system intersects any edge of the graph in at most 30 points. The existence of such short canonical systems of loops was well known in the orientable case and an open problem in the non-orientable case. Our proof techniques combine recent work of Schaefer-Štefankovič with ideas coming from computational biology, specifically from the signed reversal distance algorithm of Hannenhalli-Pevzner. The existence of short canonical non-orientable systems of loops confirms a special case of a conjecture of Negami on the joint crossing number of two embeddable graphs. We also provide a correction for an argument of Negami bounding the joint crossing number of two non-orientable graph embeddings.
