# An annotated bibliography on 1-planarity

## TL;DR

This annotated bibliography provides a comprehensive overview of 1-planar graphs, summarizing key research areas, recent developments, and open problems in the study of graphs where each edge is crossed at most once.

## Contribution

It offers a structured review of the literature on 1-planar graphs and includes a list of open problems for future research.

## Key findings

- Summarizes characterization and recognition of 1-planar graphs
- Reviews combinatorial properties and geometric representations
- Provides a list of open research problems

## Abstract

The notion of 1-planarity is among the most natural and most studied generalizations of graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at most another edge. The study of 1-planar graphs dates back to more than fifty years ago and, recently, it has driven increasing attention in the areas of graph theory, graph algorithms, graph drawing, and computational geometry. This annotated bibliography aims to provide a guiding reference to researchers who want to have an overview of the large body of literature about 1-planar graphs. It reviews the current literature covering various research streams about 1-planarity, such as characterization and recognition, combinatorial properties, and geometric representations. As an additional contribution, we offer a list of open problems on 1-planar graphs.