论文标题
最小的素数年龄，单词和置换图扩展了摘要
Minimal prime ages, words and permutation graphs Extended abstract
论文作者
论文摘要
本文是对遗传类别有限图的研究的贡献。我们根据它们所包含的主要结构数量对这些类进行分类。我们认为这样的类是\ emph {minimal prime}：包含无限很多数量但每个适当的遗传子类仅包含许多素数的类。我们给出了此类课程的完整表征。实际上，这些课程中的每一个都是准有序的年龄，并且有许多班级。当添加准准订单中的标签时，这些年龄中的11个仍然很好地排序。在其余的添加时，当添加一个标签时，数量仍然很好地排序。除六个示例外，我们表征的这些年龄的成员是置换图。实际上，每个年龄不在11个年龄段都是与整数上均匀的$ 0 $ 0 $ - $ 1 $单词相关的图表的年龄。还提供了最小的poset和折叠类别的特征。
This paper is a contribution to the study of hereditary classes of finite graphs. We classify these classes according to the number of prime structures they contain. We consider such classes that are \emph{minimal prime}: classes that contain infinitely many primes but every proper hereditary subclass contains only finitely many primes. We give a complete characterization of such classes. In fact, each one of these classes is a well quasi ordered age and there are uncountably many of them. Eleven of these ages remain well quasi ordered when labels in a well quasi ordering are added. Among the remaining ones, countably many remain well quasi ordered when one label is added. Except for six examples, members of these ages we characterize are permutation graphs. In fact, every age which is not among the eleven ones is the age of a graph associated to a uniformly recurrent $0$-$1$ word on the integers. A characterization of minimal prime classes of posets and bichains is also provided.
