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Hereditary biclique-Helly graphs: recognition and maximal biclique enumeration.
- Source :
-
Discrete Mathematics & Theoretical Computer Science (DMTCS) . 2013, Vol. 15 Issue 1, p55-74. 20p. 3 Diagrams. - Publication Year :
- 2013
-
Abstract
- A biclique is a set of vertices that induce a complete bipartite graph. A graph G is biclique-Helly when its family of maximal bicliques satisfies the Helly property. If every induced subgraph of G is also biclique-Helly, then G is hereditary biclique-Helly. A graph is C4-dominated when every cycle of length 4 contains a vertex that is dominated by the vertex of the cycle that is not adjacent to it. In this paper we show that the class of hereditary biclique-Helly graphs is formed precisely by those C4-dominated graphs that contain no triangles and no induced cycles of length either 5 or 6. Using this characterization, we develop an algorithm for recognizing hereditary biclique-Helly graphs in O(n² + αm) time and O(n+m) space. (Here n, m, and α = O(m1/2) are the number of vertices and edges, and the arboricity of the graph, respectively.) As a subprocedure, we show how to recognize those C4-dominated graphs that contain no triangles in O(αm) time and O(n + m) space. Finally, we show how to enumerate all the maximal bicliques of a C4-dominated graph with no triangles in O(n² + am) time and O(αm) space. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BIPARTITE graphs
*SUBGRAPHS
*GRAPH theory
*GEOMETRY
*ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 13658050
- Volume :
- 15
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics & Theoretical Computer Science (DMTCS)
- Publication Type :
- Academic Journal
- Accession number :
- 90174598