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2009
Springer

On Planar Supports for Hypergraphs

9 years 11 months ago
On Planar Supports for Hypergraphs
A graph G is a support for a hypergraph H = (V, S) if the vertices of G correspond to the vertices of H such that for each hyperedge Si ∈ S the subgraph of G induced by Si is connected. G is a planar support if it is a support and planar. Johnson and Pollak [9] proved that it is NPcomplete 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 2-outerplanar support.
Kevin Buchin, Marc J. van Kreveld, Henk Meijer, Be
Added 24 Jul 2010
Updated 24 Jul 2010
Type Conference
Year 2009
Where GD
Authors Kevin Buchin, Marc J. van Kreveld, Henk Meijer, Bettina Speckmann, Kevin Verbeek
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