## Maurice Pouzet ; Imed Zaguia - Graphs containing finite induced paths of unbounded length

dmtcs:6915 - Discrete Mathematics & Theoretical Computer Science, March 8, 2022, vol. 23 no. 2, special issue in honour of Maurice Pouzet - https://doi.org/10.46298/dmtcs.6915
Graphs containing finite induced paths of unbounded length

Authors: Maurice Pouzet ; Imed Zaguia

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.

Volume: vol. 23 no. 2, special issue in honour of Maurice Pouzet
Section: Special issues
Published on: March 8, 2022
Accepted on: November 15, 2021
Submitted on: November 18, 2020
Keywords: Mathematics - Combinatorics,06A6, 06F15