The Connectivity of a Bipartite Graph and Its Bipartite Complementary Graph

On Component Order Edge Connectivity Of a Complete Bipartite Graph

The traditional parameter used as a measure of vulnerability of a network modeled by a graph with perfect nodes and edges that may fail is the edge connectivity λ. Of course , () p q K p λ = where p q ≤. In that case, failure of the network simply means that the surviving subgraph becomes disconnected upon the failure of individual edges. If, instead, failure of the network is defined to mean t...

Supervised Bipartite Graph Inference

We formulate the problem of bipartite graph inference as a supervised learning problem, and propose a new method to solve it from the viewpoint of distance metric learning. The method involves the learning of two mappings of the heterogeneous objects to a unified Euclidean space representing the network topology of the bipartite graph, where the graph is easy to infer. The algorithm can be form...

Bipartite Graph Tiling

For each s ≥ 2, there exists m0 such that the following holds for all m ≥ m0: Let G be a bipartite graph with n = ms vertices in each partition set. If m is odd and minimum degree δ(G) ≥ n+3s 2 − 2, then G contains m vertex-disjoint copies of Ks,s. If m is even, the same holds under the weaker condition δ(G) ≥ n/2+ s− 1. This is sharp and much stronger than a conjecture of Wang [25] (for large n).

The Planar Algebra of a bipartite graph

Testing of bipartite graph properties ∗

Alon et. al. [3], showed that every property that is characterized by a finite collection of forbidden induced subgraphs is -testable. However, the complexity of the test is double-tower with respect to 1/ , as the only tool known to construct such tests is via a variant of Szemerédi’s Regularity Lemma. Here we show that any property of bipartite graphs that is characterized by a finite collect...