Every Poset has a Large Cut

TL;DR

This paper proves that every finite poset contains a directed cut capturing at least half of its order relations, and provides an efficient linear-time algorithm to find such a cut.

Contribution

It establishes a tight bound on the size of the largest directed cut in any finite poset and presents a linear-time algorithm for finding it.

Findings

Every finite poset has a directed cut with at least half of the order relations.

The bound on the size of the directed cut is tight.

The largest directed cut can be found in linear time.

Abstract

We prove that every finite poset has a directed cut with at least one half of the poset's pairwise order relations. The bound is tight. Also, the largest directed cut in a poset can be found in linear time.