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We consider hypergraph visualization that represent vertices as points and hyperedges as lines with few bends passing through points of their incident vertices. Guided by point-line incidence theory we show several theoretical results: if every vertex is part of at most two hyperedges, then we can find such a visualization without bends. There exist hypergraphs with three vertices per hyperedge and three hyperedges incident to each vertex requiring an arbitrary number of bends. It is ETR-hard to decide whether an arbitrary hypergraph can be visualized without bends. This only answers some interesting questions for such visualizations and we conclude with many open research questions.more » « less
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