Vertex removal in biclique graphs
Discrete Mathematics
2022-05-31 v3
Abstract
A \textit{biclique} is a maximal induced complete bipartite subgraph. The \textit{biclique graph} of a graph , denoted by , is the intersection graph of the family of all bicliques of . In this work we address the following question: Given a biclique graph , is it possible to remove a vertex of , such that is a biclique graph? And if possible, can we obtain a graph such that ? We show that the general question has a "no" for answer. However, we prove that if has a vertex such that , then is a biclique graph and we show how to obtain .
Cite
@article{arxiv.2006.04583,
title = {Vertex removal in biclique graphs},
author = {Leandro Montero},
journal= {arXiv preprint arXiv:2006.04583},
year = {2022}
}