Fabrizio Montecchiani

Recognizing and Drawing IC-Planar Graphs

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossedi¾?at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graphi¾?G withi¾?n vertices, we present an On-time algorithm that computes a straight-line drawing ofi¾?G in quadratic area, and an

Fan-planarity

On^3

Area requirement of graph drawings with few crossings per edge

-time algorithm that computes a straight-line drawing ofi¾?G with right-angle crossings in exponential area. Both these area requirements are worst-case optimal. We also show that it is

An advanced network visualization system for financial crime detection

mathrm {NP}

L-visibility drawings of IC-planar graphs

-complete to test IC-planarity both in the general case and in the case in which a rotation system is fixed for the input graph. Furthermore, we describe a polynomial-time algorithm to test whether a set of matching edges can be added to a triangulated planar graph such that the resulting graph is IC-planar.

Fast Layout Computation of Hierarchically Clustered Networks: Algorithmic Advances and Experimental Analysis

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.