2020/06/08 by Leandro Montero, Montero, Leandro
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · doi:10.48550/arxiv.2006.04583
openalex publication_date 2020/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A biclique is a maximal induced complete bipartite subgraph. The biclique graph of a graph H, denoted by KB(H), is the intersection graph of the family of all bicliques of H. In this work we address the following question: Given a biclique graph G=KB(H), is it possible to remove a vertex q of G, such that G - \q\ is a biclique graph? And if possible, can we obtain a graph H' such that G - \q\ = KB(H')? We show that the general question has a "no" for answer. However, we prove that if G has a vertex q such that d(q) = 2, then G-\q\ is a biclique graph and we show how to obtain H'.