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arXiv · 2505.16837

Dimension of unicycle posets

Antoine Abram·Adrien Segovia
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Abstract

Motivated by the study of the dimension of random posets, it was conjectured by Bollobás and Brightwell in 1997 that if $P$ is a finite poset whose cover graph contains at most one cycle then its order dimension is at most $3$. In this paper we prove this conjecture by giving a constructive proof with explicit triplets of linear extensions realizing such posets.

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Antoine Abram, Adrien Segovia. 2026-06-09. Dimension of unicycle posets. https://arxiv.org/abs/2505.16837

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