**Confluent drawings: visualizing non-planar diagrams in a planar way**.

M. Dickerson, D. Eppstein, M. T. Goodrich, and J. Meng.

arXiv:cs.CG/0212046.

11th Int. Symp. Graph Drawing, Perugia, Italy, 2003.

Springer,*Lecture Notes in Comp. Sci.*2912, 2004, pp. 1–12.

*J. Graph Algorithms and Applications*(special issue for GD'03) 9 (1): 31–52, 2005.We describe a new method of drawing graphs, based on allowing the edges to be merged together and drawn as "tracks" (similar to train tracks). We present heuristics for finding such drawings based on my previous algorithms for finding maximal bipartite subgraphs, prove that several important families of graphs have confluent drawings, and provide examples of other graphs that can not be drawn in this way.

**Confluent layered drawings**.

D. Eppstein, M. T. Goodrich, and J. Meng.

12th Int. Symp. Graph Drawing, New York, 2004.

Springer,*Lecture Notes in Comp. Sci.*3383, 2004, pp. 184–194.

arXiv:cs.CG/0507051.

*Algorithmica*47 (4): 439–452 (special issue for Graph Drawing), 2007.Describes a graph drawing technique combining ideas of confluent drawing with Sugiyama-style layered drawing. Uses a reduction to graph coloring to find and visualize sets of bicliques in each layer.

**Delta-confluent drawings**.

D. Eppstein, M. T. Goodrich, and J. Meng.

13th Int. Symp. Graph Drawing, Limerick, Ireland, 2005.

Springer,*Lecture Notes in Comp. Sci.*3843, 2006, pp. 165–176.

arXiv:cs.CG/0510024.

We characterize the graphs that can be drawn confluently with a single confluent track that is tree-like except for three-way Delta junctions, as being exactly the distance hereditary graphs. Based on this characterization, we develop efficient algorithms for drawing these graphs.

Co-authors – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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