论文标题
星星和梳子III的双重定理：未主导的梳子
Duality theorems for stars and combs III: Undominated combs
论文作者
论文摘要
在一系列四篇论文中，我们确定了其存在是偶性的结构，从互补的意义上讲，对恒星或梳子的存在。在这里，在该系列的第三篇论文中，我们提出了二元定理，以结合恒星和梳子：未主导的梳子。我们用无射线树和树状分解来描述它们的互补结构。 应用程序包括按照正常的跨越树的完整表征，其射线被主导但没有无光线跨越树的图。到目前为止，仅西摩和托马斯以及托马森只构建了两个这样的图。作为推论，我们表明，当且仅当它们所有的射线都占主导时，具有普通生成树的图形具有无射线的跨越树。
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. Here, in the third paper of the series, we present duality theorems for a combination of stars and combs: undominated combs. We describe their complementary structures in terms of rayless trees and of tree-decompositions. Applications include a complete characterisation, in terms of normal spanning trees, of the graphs whose rays are dominated but which have no rayless spanning tree. Only two such graphs had so far been constructed, by Seymour and Thomas and by Thomassen. As a corollary, we show that graphs with a normal spanning tree have a rayless spanning tree if and only if all their rays are dominated.
