Dimension of CPT posets
Atrayee Majumder, Rogers Mathew, Deepak Rajendraprasad

TL;DR
This paper investigates the dimension of containment posets derived from paths in trees (CPT posets), providing bounds based on the host tree's properties and presenting an efficient algorithm for a specific poset class.
Contribution
It establishes asymptotically tight bounds on the dimension of CPT posets relative to host tree parameters and introduces a near-optimal construction algorithm for a particular poset family.
Findings
Dimension bound depends on host tree degree and radius.
Bound is asymptotically tight up to a small additive factor.
Algorithm constructs near-optimal realizers for the poset of 1- and 2-element subsets.
Abstract
A collection of linear orders on , say , is said to \emph{realize} a partially ordered set (or poset) if, for any two distinct , if and only if , . We call a \emph{realizer} of . The \emph{dimension} of , denoted by , is the minimum cardinality of a realizer of . A \emph{containment model} of a poset maps every to a set such that, for every distinct if and only if . We shall be using the collection to identify the containment model . A poset is a Containment order of Paths in a Tree (CPT poset), if it admits a containment model…
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