生成点三价图和点三角形地图的一个优化算法
An Optimal Algorithm to Generate Pointed Trivalent Diagrams and Pointed Triangular Maps
摘要：
三价图是一个连通的双色二部图（允许平行边，但不允许循环），使得每个黑色顶点的度为1或3，每个白色顶点的度为1或2，并对每个与同一顶点相关的边集施加循环顺序。有根的三价图是一个有一个明显的边，它的根的三价图。我们将描述和分析一个算法，给出一个给定大小（边数）的有根三价图的穷举列表，该列表是非冗余的，因为列表中没有两个图是同构的。该算法将被证明具有最佳的性能，在必要的时间来生成一个图将被视为有界的摊销意义上，边界是独立的图的大小。这就是我们所说的猫的财产。本文的一个目标是提供一个可重用的理论框架，算法生成复杂的组合结构的穷举列表，注意的情况下，无标签的结构和那些发电机具有CAT属性。
英文摘要：
A trivalent diagram is a connected, two-colored bipartite graph (parallel edges allowed but not loops) such that every black vertex is of degree 1 or 3 and every white vertex is of degree 1 or 2, with a cyclic order imposed on every set of edges incident to to a same vertex. A rooted trivalent diagram is a trivalent diagram with a distinguished edge, its root. We shall describe and analyze an algorithm giving an exhaustive list of rooted trivalent diagrams of a given size (number of edges), the list being non-redundant in that no two diagrams of the list are isomorphic. The algorithm will be shown to have optimal performance in that the time necessary to generate a diagram will be seen to be bounded in the amortized sense, the bound being independent of the size of the diagrams. That's what we call the CAT property. One objective of the paper is to provide a reusable theoretical framework for algorithms generating exhaustive lists of complex combinatorial structures with attention paid to the case of unlabeled structures and to those generators having the CAT property.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
