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| Format: | Preprint |
| Veröffentlicht: |
2020
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| Online-Zugang: | https://arxiv.org/abs/2011.00352 |
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| _version_ | 1866916122562920448 |
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| author | Pouzet, Maurice Zaguia, Imed |
| author_facet | Pouzet, Maurice Zaguia, Imed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_00352 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Graphs containing finite induced paths of unbounded length Pouzet, Maurice Zaguia, Imed Combinatorics 06A6, 06F15 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. |
| title | Graphs containing finite induced paths of unbounded length |
| topic | Combinatorics 06A6, 06F15 |
| url | https://arxiv.org/abs/2011.00352 |