论文标题
包含有限诱导长度的有限诱导路径的图
Graphs containing finite induced paths of unbounded length
论文作者
论文摘要
图$ g $的年龄$ \ MATHCAL {a}（g）$（无方向性且无环）是有限诱导的$ g $的收集，被认为是同构的，并通过嵌入性订购。如果不包含无限的抗抗，它是该顺序的序列序列（WQO）。图形为\ emph {path-minimal}，如果它包含有限的诱发长度的路径，并且此属性嵌入了$ g $的每个引起的子图$ g'$。我们构造$ 2^{\ aleph_0} $路径最小图，其年龄与SET包含和WQO成对无与伦比。我们的构建基于标记图的均匀复发序列和词典图。
The age $\mathcal{A}(G)$ of a graph $G$ (undirected and without loops) is the collection of finite induced subgraphs of $G$, considered up to isomorphy and ordered by embeddability. It is well-quasi-ordered (wqo) for this order if it contains no infinite antichain. A graph is \emph{path-minimal} if it contains finite induced paths of unbounded length and every induced subgraph $G'$ with this property embeds $G$. We construct $2^{\aleph_0}$ path-minimal graphs whose ages are pairwise incomparable with set inclusion and which are wqo. Our construction is based on uniformly recurrent sequences and lexicographical sums of labelled graphs.
