Distances between bicliques and structural properties of biclique graphs Marina Groshaus Universidad de Buenos Aires Departamento de ComputaciĀ“ on groshaus@dc.uba.ar Leandro Montero lpmontero@gmail.com ABSTRACT A biclique is a maximal bipartite complete induced subgraph of G. The 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 deļ¬nition of the distance between bicliques in a graph. We give a 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 graphs and properties of the biclique graph. Next, for biclique graphs that are neither a K 3 nor a diamond, we prove that the number of vertices of degree two is less than half of its vertices and we present some forbidden structures. Finally, we present some interesting related conjetures and open problems. Keywords: Bicliques; Biclique graphs; Distances in graphs, Intersection graphs, Forbidden structures arXiv:1708.09686v2 [cs.DM] 21 Oct 2018