平面四次剖分的二元标号及其关系
Binary Labelings for Plane Quadrangulations and their Relatives
摘要：
出于双射平面三角剖分和分区的内部边缘成三棵树的施奈德标号之间，我们寻找二进制标签四边形（其边缘可以划分成两棵树）。我们的标签类似于许多的属性Schnyder的一个三角：除了在双射与树分解，在这些树中的路径允许定义的顶点的区域，这样计数面在他们产生一个算法嵌入四边形，在这种情况下，在一个~2-书。此外，由于Schnyder标号已经扩展到3-连通平面图，我们能够将我们的标号从四边形图扩展到更大的一类2-连通二部图。最后，我们提出了一个二元标号的拉曼图。
英文摘要：
Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our labeling resembles many of the properties of Schnyder's one for triangulations: Apart from being in bijection with tree decompositions, paths in these trees allow to define the regions of a vertex such that counting faces in them yields an algorithm for embedding the quadrangulation, in this case on a~2-book. Furthermore, as Schnyder labelings have been extended to 3-connected plane graphs, we are able to extend our labeling from quadrangulations to a larger class of 2-connected bipartite graphs. Finally, we propose a binary labeling for Laman graphs.
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。
