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arXiv · 2209.03893

A Proof of the Alternate Thomassé Conjecture for Countable $NE$-Free Posets

Davoud Abdi
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Abstract

An $N$-free poset is a poset whose comparability graph does not embed an induced path with four vertices. We use the well-quasi-order property of the class of countable $N$-free posets and some labelled ordered trees to show that a countable $N$-free poset has one or infinitely many siblings, up to isomorphism. This, partially proves a conjecture stated by Thomassé for this class.

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Davoud Abdi. 2023-01-06. A Proof of the Alternate Thomassé Conjecture for Countable $NE$-Free Posets. https://arxiv.org/abs/2209.03893

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