A Proof of the Alternate Thomass\'e Conjecture for Countable $NE$-Free Posets

Davoud Abdi

A Proof of the Alternate Thomass\'e Conjecture for Countable $NE$-Free Posets

Combinatorics 2023-01-09 v2

Authors: Davoud Abdi

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 Thomass\'e for this class.

Keywords

N-free poset well-quasi-order labelled ordered tree siblings isomorphism Thomassé conjecture

Cite

@article{arxiv.2209.03893,
  title  = {A Proof of the Alternate Thomass\'e Conjecture for Countable $NE$-Free Posets},
  author = {Davoud Abdi},
  journal= {arXiv preprint arXiv:2209.03893},
  year   = {2023}
}

Comments

35 pages. arXiv admin note: text overlap with arXiv:2004.12457 by other authors

A Proof of the Alternate Thomass\'e Conjecture for Countable $NE$-Free Posets

Abstract

Keywords

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