Recognizing string graphs in NP
Journal of Computer and System Sciences - STOC 2002
Biclique edge cover graphs and confluent drawings
GD'06 Proceedings of the 14th international conference on Graph drawing
GD'05 Proceedings of the 13th international conference on Graph Drawing
Mad at edge crossings? break the edges!
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
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Confluent graphs capture the connection properties of train tracks, offering a very natural generalization of planar graphs, and – as the example of railroad maps shows – are an important tool in graph visualization. In this paper we continue the study of confluent graphs, introducing strongly confluent graphs and tree-confluent graphs. We show that strongly confluent graphs can be recognized in NP (the complexity of recognizing confluent graphs remains open). We also give a natural elimination ordering characterization of tree-confluent graphs which shows that they form a subclass of the chordal bipartite graphs, and can be recognized in polynomial time.