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 |
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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 |
| _version_ | 1797270011851571200 |
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| author | Maurice Pouzet Imed Zaguia |
| author_facet | Maurice Pouzet Imed Zaguia |
| author_sort | Maurice Pouzet |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T21:31:52Z |
| format | Article |
| id | doaj.art-7f065a63e2bd41628e67184136f9a414 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:57:29Z |
| publishDate | 2022-03-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-7f065a63e2bd41628e67184136f9a4142024-03-07T15:44:44ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502022-03-01vol. 23 no. 2, special issue...Special issues10.46298/dmtcs.69156915Graphs containing finite induced paths of unbounded lengthMaurice PouzetImed ZaguiaThe 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.https://dmtcs.episciences.org/6915/pdfmathematics - combinatorics06a6, 06f15 |
| spellingShingle | Maurice Pouzet Imed Zaguia Graphs containing finite induced paths of unbounded length Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics 06a6, 06f15 |
| title | Graphs containing finite induced paths of unbounded length |
| title_full | Graphs containing finite induced paths of unbounded length |
| title_fullStr | Graphs containing finite induced paths of unbounded length |
| title_full_unstemmed | Graphs containing finite induced paths of unbounded length |
| title_short | Graphs containing finite induced paths of unbounded length |
| title_sort | graphs containing finite induced paths of unbounded length |
| topic | mathematics - combinatorics 06a6, 06f15 |
| url | https://dmtcs.episciences.org/6915/pdf |
| work_keys_str_mv | AT mauricepouzet graphscontainingfiniteinducedpathsofunboundedlength AT imedzaguia graphscontainingfiniteinducedpathsofunboundedlength |