A Note on d-Biclique Covers

A d-biclique cover of a graph G is a collection of bicliques of G such that each edge of G is in at least d of the bicliques. The number of bicliques in a minimum d-biclique cover of G is called the d-biclique covering number of G and is denoted by \({bc}_d(G)\). In this paper, we present an upper b...

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Bibliographic Details
Published in:arXiv.org 2012-07
Main Authors: Moazami, Farokhlagha, Soltankhah, Nasrin, Basiriz, Shahzad
Format: Article
Language:English
Subjects:
Graphs
Upper bounds
Online Access:Get full text
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Summary:A d-biclique cover of a graph G is a collection of bicliques of G such that each edge of G is in at least d of the bicliques. The number of bicliques in a minimum d-biclique cover of G is called the d-biclique covering number of G and is denoted by \({bc}_d(G)\). In this paper, we present an upper bound for the d- biclique covering number of the lexicographic product of graphs. Also, we introduce some bounds of this parameter for some graph constructions and obtain the exact value of the d-biclique covering number of some graphs.
ISSN:2331-8422