On edge-sets of bicliques in graphs
A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-sets of all bicliques. We characterize graphs...
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| Autores principales: | , , |
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| Formato: | Artículo publishedVersion |
| Lenguaje: | Inglés |
| Publicado: |
2012
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| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0166218X_v160_n18_p2698_Groshaus |
| Aporte de: |
| Sumario: | A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-sets of all bicliques. We characterize graphs whose edge-biclique hypergraph is conformal (i.e., it is the clique hypergraph of its 2-section) by means of a single forbidden induced obstruction, the triangular prism. Using this result, we characterize graphs whose edge-biclique hypergraph is Helly and provide a polynomial time recognition algorithm. We further study a hereditary version of this property and show that it also admits polynomial time recognition, and, in fact, is characterized by a finite set of forbidden induced subgraphs. We conclude by describing some interesting properties of the 2-section graph of the edge-biclique hypergraph. © 2011 Elsevier B.V. All rights reserved. |
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