Abstract
A graph G is a support for a hypergraph \(H = (V, \mathcal{S})\) if the vertices of G correspond to the vertices of H such that for each hyperedge \(S_i \in \mathcal{S}\) the subgraph of G induced by S i is connected. G is a planar support if it is a support and planar. Johnson and Pollak [9] proved that it is NP-complete to decide if a given hypergraph has a planar support. In contrast, there are polynomial time algorithms to test whether a given hypergraph has a planar support that is a path, cycle, or tree. In this paper we present an algorithm which tests in polynomial time if a given hypergraph has a planar support that is a tree where the maximal degree of each vertex is bounded. Our algorithm is constructive and computes a support if it exists. Furthermore, we prove that it is already NP-hard to decide if a hypergraph has a 3-outerplanar support.
K. Buchin, B. Speckmann, and K. Verbeek were supported by the Netherlands’ Organisation for Scientific Research (NWO) under project no. 639.022.707.
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Buchin, K., van Kreveld, M., Meijer, H., Speckmann, B., Verbeek, K. (2010). On Planar Supports for Hypergraphs. In: Eppstein, D., Gansner, E.R. (eds) Graph Drawing. GD 2009. Lecture Notes in Computer Science, vol 5849. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11805-0_33
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DOI: https://doi.org/10.1007/978-3-642-11805-0_33
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