Journal of Graph Algorithms and Applications
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On Planar Supports for Hypergraphs
Vol. 15, no. 4, pp. 533-549, 2011. Regular paper.
Abstract 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  proved that it is NP-complete to decide if a given hypergraph has a planar support. In contrast, there are lienar 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 efficient 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.
Submitted: January 2010.
Reviewed: January 2011.
Revised: June 2011.
Accepted: August 2011.
Final: September 2011.
Published: September 2011.
Communicated by Michael Kaufmann