Graphs containing finite induced paths of unbounded length
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2022-03-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/6915/pdf |
| Summary: | 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. |
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| ISSN: | 1365-8050 |