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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Acknowledgements
I would like to thank my PhD supervisors Professor Robert Woodrow and Professor Claude Laflamme for suggesting this problem and for their help and advice.
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This paper is a project as part of author’s thesis under supervision of Dr. Claude Laflamme and Dr. Robert Woodrow at the Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada (2017-2022).
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Abdi, D. A Proof of the Alternate Thomassé Conjecture for Countable N-Free Posets. Order (2023). https://doi.org/10.1007/s11083-023-09650-w
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DOI: https://doi.org/10.1007/s11083-023-09650-w