English

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 HH, denoted by KB(H)KB(H), is the intersection graph of the family of all bicliques of HH. In this work we address the following question: Given a biclique graph G=KB(H)G=KB(H), is it possible to remove a vertex qq of GG, such that G{q}G - \{q\} is a biclique graph? And if possible, can we obtain a graph HH' such that G{q}=KB(H)G - \{q\} = KB(H')? We show that the general question has a "no" for answer. However, we prove that if GG has a vertex qq such that d(q)=2d(q) = 2, then G{q}G-\{q\} is a biclique graph and we show how to obtain HH'.

Cite

@article{arxiv.2006.04583,
  title  = {Vertex removal in biclique graphs},
  author = {Leandro Montero},
  journal= {arXiv preprint arXiv:2006.04583},
  year   = {2022}
}
R2 v1 2026-06-23T16:08:44.313Z