Tight lower bounds on the number of bicliques in false-twin-free graphs

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• 作者：Marina Groshaus^a ; ^{groshaus@dc.uba.ar" class="auth_mail" title="E-mail the corresponding author} ; Leandro Montero^b ; ^{lmontero@lri.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Bicliques ; False-twin-free graphs ; Lower bounds
• 刊名：Electronic Notes in Discrete Mathematics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：50
• 期：Complete
• 页码：293-298
• 全文大小：191 K

文摘

A biclique is a maximal bipartite complete induced subgraph of G. Bicliques have been studied in the last years motivated by the large number of applications. In particular, enumeration of the maximal bicliques has been of interest in data analysis. Associated with this issue, upper and lower bounds on the maximun number of bicliques were given. In this paper we study lower bounds on the number of bicliques of a graph. Since adding false-twin vertices to G   does not change the number of bicliques, we restrict to false-twin-free graphs. We give a tight lower bound on the minimum number bicliques in {C₄$C_4$,diamond,false-twin}-free graphs, {K₃$K_3$,false-twin}-free graphs and we present some conjectures for general false-twin-free graphs.