Geodesic
Graphs containing finite induced paths of unbounded length
Discrete mathematics & theoretical computer science, special issue in honour of Maurice Pouzet, Tome 23 (2021-2022) no. 2.

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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.
DOI : 10.46298/dmtcs.6915
Classification : 05C12, 05C38, 05C60, 05C78, 06A07, 68R15 
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     title = {Graphs containing finite induced paths of unbounded length},
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Pouzet, Maurice; Zaguia, Imed. Graphs containing finite induced paths of unbounded length. Discrete mathematics & theoretical computer science, special issue in honour of Maurice Pouzet, Tome 23 (2021-2022) no. 2. doi : 10.46298/dmtcs.6915. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6915/

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