C4-saturated bipartite graphs

Complexity of minimum biclique decomposition of bipartite graphs

Many problems studied in graph theory are graph decomposition problems. The minimum number of complete bipartite graphs needed to partition the edges of a bipartite graph. is one of these problem and it is still open. We propose a NP-completness proof for its decision version and we show that it is polynomial on bipartite C4-free graphs.

On the Complete Width and Edge Clique Cover Problems

A complete graph is the graph in which every two vertices are adjacent. For a graph G = (V,E), the complete width of G is the minimum k such that there exist k independent sets Ni ⊆ V , 1 ≤ i ≤ k, such that the graph G obtained from G by adding some new edges between certain vertices inside the sets Ni, 1 ≤ i ≤ k, is a complete graph. The complete width problem is to decide whether the complete...

C4-1: Building a community hierarchy for the Web based on Bipartite Graphs

META-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS

The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...

Bipartite decomposition of random graphs

Definition (Maximal size complete bipartite induced subgraph). β(G) := size of maximal complete bipartite induced subgraph of G. Definition (Minimal bipartite decomposion number). τ(G) := minimal number of complete edge disjoint covering bipartite subgraphs of G. Definition (Minimal nontrivial bipartite decomposion number). τ (G) := minimal number of complete edge disjoint covering nontrivial (...