Combinatorial characterization of upward planarity

TL;DR

This paper provides a combinatorial framework for understanding upward planar graphs by introducing upward planar orders, which are specific linear extensions of edge posets, offering a new way to characterize these graphs.

Contribution

It introduces the concept of upward planar orders as a novel combinatorial characterization of upward planar graphs, linking graph planarity with order theory.

Findings

Characterization of upward planar graphs using upward planar orders

Establishment of a correspondence between upward planarity and linear extensions of edge posets

New combinatorial tools for analyzing upward planarity

Abstract

We give a combinatorial characterization of upward planar graphs in terms of upward planar orders, which are special linear extensions of edge posets.