Distances between bicliques and structural properties of bicliques in graphs.
Marina Groshaus, Leandro P. Montero · arXiv (Cornell University) · 2017
A \emph{biclique} is a maximal bipartite complete induced subgraph of $G$. The \emph{biclique graph} of a graph $G$, denoted by $KB(G)$, is the intersection graph of the family of all bicliques of $G$. In this work we give a natural definition of the distance between bicliques in a graph. We give a useful formula that relates the distance between bicliques in a graph $G$ and the distance between their respectives vertices in $KB(G)$. As application of the concept of the distance between bicliques, we show some results about the structure of bicliques in a graph and properties of the biclique graph. We obtain some corollaries from this result and finally we present some interesting related open problems.