Graphs containing finite induced paths of unbounded length

Maurice Pouzet; Imed Zaguia

doi:10.46298/dmtcs.6915

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 lengthArticle

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.

Comment: 28 pages, 3 figures

https://doi.org/10.46298/dmtcs.6915

Source: arXiv.org:2011.00352

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

Licence: arXiv.org - Non-exclusive license to distribute

Funding:

Source : OpenAIRE Graph