Almost every graph is divergent under the biclique operator

@article{Groshaus2016AlmostEG,
  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.},
  year={2016},
  volume={201},
  pages={130-140}
}
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11 Citations
Background Citations
3
Methods Citations
1

11 Citations

On the Iterated Edge-Biclique Operator
On the edge‐biclique graph and the iterated edge‐biclique operator
TLDR
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
On bicliques and the second clique graph of suspensions
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
TLDR
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.
...
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References

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On the Iterated Biclique Operator
TLDR
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 number of convergent graphs under the biclique operator with no twin vertices is finite
Whitney triangulations, local girth and iterated clique graphs
On the generation of bicliques of a graph
Generating bicliques of a graph in lexicographic order
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
TLDR
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.
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