Almost every graph is divergent under the biclique operator

  title={Almost every graph is divergent under the biclique operator},
  author={Marina Groshaus and Andr{\'e} Luiz Pires Guedes and Leandro Montero},
  journal={Discret. Appl. Math.},
On the edge‐biclique graph and the iterated edge‐biclique operator
The sufficient conditions for a graph to be convergent or divergent under the operator $KB_e$ are given and the behavior ofgeon graphs is characterized and some general conjectures on the subject are proposed.
Biclique Graphs of K3-free Graphs and Bipartite Graphs
Intersection graph of maximal stars
Biclique graphs of interval bigraphs
On cliques and bicliques
Biclique graph of bipartite permutation graphs
Clique‐convergence is undecidable for automatic graphs
The clique operator transforms a graph G into its clique graph K ( G ) , which is the intersection graph of all the (maximal) cliques of G . Iterated clique graphs are then defined by K n ( G ) = K (
Quelques problèmes d'algorithmique et combinatoires en théorie des grapphes. (A Few Problems of Algorithm and Complexity in Graph Theory)
  • S. Legay
  • Philosophy, Computer Science
  • 2017
Cette these traite de differents problemes de decisions binaires ou de minimisations lies a la notion of graphe, et cherche, pour chacun of ces problemes, a determiner sa classe de complexite, ou a fournir un algorithme.


On the Iterated Biclique Operator
A forbidden structure characterization of convergent graphs, which yield a polynomial time algorithm to decide if a given graph diverges or converges under the biclique operator.
The clique operator on cographs and serial graphs
Locally C6 graphs are clique divergent
Equivariant collapses and the homotopy type of iterated clique graphs
The icosahedron is clique divergent
Efficient Mining of Large Maximal Bicliques
This paper proposes an efficient algorithm to mine large maximal biclique subgraphs from undirected graphs using a divide-and-conquer approach and shows that the proposed algorithm outperforms previous work significantly.