Embedding Quartic Eulerian Digraphs on the Plane

TL;DR

This paper investigates the minimal obstructions for embedding 4-regular Eulerian digraphs on the plane, classifying those with parallel arcs and analyzing their properties within a cycle removal partial order.

Contribution

It provides a classification of all obstructions with parallel arcs and explores their properties in the context of planar embeddings of Eulerian digraphs.

Findings

Classified all obstructions with parallel arcs.

Analyzed properties of minimal obstructions.

Connected obstructions to cycle removal order.

Abstract

Minimal obstructions for embedding 4-regular Eulerian digraphs on the plane are considered in relation to the partial order defined by the cycle removal operation. Their basic properties are provided and all obstructions with parallel arcs are classified.