709 research outputs found
A Coloring Algorithm for Disambiguating Graph and Map Drawings
Drawings of non-planar graphs always result in edge crossings. When there are
many edges crossing at small angles, it is often difficult to follow these
edges, because of the multiple visual paths resulted from the crossings that
slow down eye movements. In this paper we propose an algorithm that
disambiguates the edges with automatic selection of distinctive colors. Our
proposed algorithm computes a near optimal color assignment of a dual collision
graph, using a novel branch-and-bound procedure applied to a space
decomposition of the color gamut. We give examples demonstrating the
effectiveness of this approach in clarifying drawings of real world graphs and
maps
Fixed parameter tractability of crossing minimization of almost-trees
We investigate exact crossing minimization for graphs that differ from trees
by a small number of additional edges, for several variants of the crossing
minimization problem. In particular, we provide fixed parameter tractable
algorithms for the 1-page book crossing number, the 2-page book crossing
number, and the minimum number of crossed edges in 1-page and 2-page book
drawings.Comment: Graph Drawing 201
Drawing Graphs with Circular Arcs and Right-Angle Crossings
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 Tur\'an-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
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