Level Planarity: Transitivity vs. Even Crossings

TL;DR

This paper establishes a connection between Hanani-Tutte theorems and level planarity testing, leading to a new polynomial-time algorithm for radial level planarity.

Contribution

It proves the equivalence of 2-Sat formulation and Hanani-Tutte theorem for level planarity, extending to radial level planarity and providing an efficient testing algorithm.

Findings

Proves equivalence between 2-Sat formulation and Hanani-Tutte theorem for level planarity.

Extends results to radial level planarity, establishing a polynomial-time testing algorithm.

Provides a new theoretical foundation linking crossing properties and planarity testing.

Abstract

Recently, Fulek et al. have presented Hanani-Tutte results for (radial) level planarity, i.e., a graph is (radial) level planar if it admits a (radial) level drawing where any two (independent) edges cross an even number of times. We show that the 2-Sat formulation of level planarity testing due to Randerath et al. is equivalent to the strong Hanani-Tutte theorem for level planarity. Further, we show that this relationship carries over to radial level planarity, which yields a novel polynomial-time algorithm for testing radial level planarity.