The Edge Covering Number of Ordered Sets

Abstract

The edge covering number $e(P)$ of an ordered set $P$ is the minimum number of suborders of $P$ of dimension at most two so that every covering edge of $P$ is included in one of the suborders. Unlike other familiar decompositions, we can reconstruct the ordered set $P$ from its components. In this paper, we find some familiar ordered sets of edge covering number two and then show that $e(2^n)\to \mathrm{\infty }$ as $n$ gets large.