Log In Sign Up

Drawing Graphs with Circular Arcs and Right-Angle Crossings

by   Steven Chaplick, et al.

In a RAC drawing of a graph, vertices are represented by points in the plane, adjacent vertices are connected by line segments, and crossings must form right angles. Graphs that admit such drawings are RAC graphs. RAC graphs are beyond-planar graphs and have been studied extensively. In particular, it is known that a RAC graph with n vertices has at most 4n - 10 edges. We introduce a superclass of RAC graphs, which we call arc-RAC graphs. A graph is arc-RAC if it admits a drawing where edges are represented by circular arcs and crossings form right angles. We provide a Turán-type result showing that an arc-RAC graph with n vertices has at most 14n - 12 edges and that there are n-vertex arc-RAC graphs with 4.5n - o(n) edges.


page 1

page 2

page 3

page 4


Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends

We study the following classes of beyond-planar graphs: 1-planar, IC-pla...

On RAC Drawings of Graphs with one Bend per Edge

A k-bend right-angle-crossing drawing or (k-bend RAC drawing, for short)...

Bipartite and Series-Parallel Graphs Without Planar Lombardi Drawings

We find a family of planar bipartite graphs all of whose Lombardi drawin...

On Strict (Outer-)Confluent Graphs

A strict confluent (SC) graph drawing is a drawing of a graph with verti...

Lombardi Drawings of Knots and Links

Knot and link diagrams are projections of one or more 3-dimensional simp...

Minimizing Crossings in Constrained Two-Sided Circular Graph Layouts

Circular layouts are a popular graph drawing style, where vertices are p...

Rule-Based Drawing, Analysis and Generation of Graphs for Mason's Mark Design

We are developing a rule-based implementation of a tool to analyse and g...