3 research outputs found
Planar and Poly-Arc Lombardi Drawings
In Lombardi drawings of graphs, edges are represented as circular arcs, and
the edges incident on vertices have perfect angular resolution. However, not
every graph has a Lombardi drawing, and not every planar graph has a planar
Lombardi drawing. We introduce k-Lombardi drawings, in which each edge may be
drawn with k circular arcs, noting that every graph has a smooth 2-Lombardi
drawing. We show that every planar graph has a smooth planar 3-Lombardi drawing
and further investigate topics connecting planarity and Lombardi drawings.Comment: Expanded version of paper appearing in the 19th International
Symposium on Graph Drawing (GD 2011). 16 pages, 8 figure
Biclique Edge Cover Graphs and Confluent Drawings
Confluent drawing is a technique that allows some non-planar
graphs to be visualized in a planar way. This approach merges
edges together, drawing groups of them as single tracks,
similar to train tracks. In the general case, producing confluent
drawings automatically has proven quite difficult. We introduce
the biclique edge cover graph that represents a graph G as an
interconnected set of cliques and bicliques. We do this in such a
way as to permit a straightforward transformation to a confluent
drawing of G. Our result is a new sufficient condition for
confluent planarity and an additional algorithmic approach for
generating confluent drawings. We give some experimental results
gauging the performance of existing confluent drawing heuristics