星与梳的对偶定理III：非支配梳
Duality theorems for stars and combs III: Undominated combs
摘要：
在一系列的四个文件，我们确定结构的存在是双重的，在这个意义上的补充，存在的恒星或梳子。在这里，在该系列的第三篇论文，我们提出了对偶定理的组合的明星和梳子：非支配梳子。我们描述他们的互补结构的无射线树和树分解。应用程序包括一个完整的表征，在正常的生成树，图的射线占主导地位，但没有rayless生成树。只有两个这样的图已建成迄今为止，西摩和托马斯和阿森。作为推论，我们证明了具有正常生成树的图具有无射线生成树当且仅当其所有射线都是支配的。
英文摘要：
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.
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