Twins in Subdivision Drawings of Hypergraphsvan Bevern, René and Kanj, Iyad and Komusiewicz, Christian and Niedermeier, Rolf and Sorge, Manuel (2016) Twins in Subdivision Drawings of Hypergraphs. In: Graph Drawing and Network Visualization. GD 2016, September, 19.  21., 2016 , pp. 6780(Official URL: http://dx.doi.org/10.1007/9783319501062_6). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783319501062_6
AbstractVisualizing hypergraphs, systems of subsets of some universe, has continuously attracted research interest in the last decades. We study a natural kind of hypergraph visualization called subdivision drawings. Dinkla et al. [Comput. Graph. Forum ’12] claimed that only few hypergraphs have a subdivision drawing. However, this statement seems to be based on the assumption (also used in previous work) that the input hypergraph does not contain twins, pairs of vertices which are in precisely the same hyperedges (subsets of the universe). We show that such vertices may be necessary for a hypergraph to admit a subdivision drawing. As a counterpart, we show that the number of such “necessary twins” is upperbounded by a function of the number m of hyperedges and a further parameter r of the desired drawing related to its number of layers. This leads to a lineartime algorithm for determining such subdivision drawings if m and r are constant; in other words, the problem is lineartime fixedparameter tractable with respect to the parameters m and r.
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