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 [11] proved that it is NPcomplete 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 e¿cient 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.
Original language | English |
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Pages (from-to) | 533-549 |
Journal | Journal of Graph Algorithms and Applications |
Volume | 15 |
Issue number | 4 |
Publication status | Published - 2011 |