Dimension of unicycle posets

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.

arXiv comment19 pages