The bipartite-splittance of a bipartite graph

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...

Note on Bipartite Graph Tilings

Let s < t be two fixed positive integers. We determine sufficient minimum degree conditions for a bipartite graph G, with both color classes of size n = k(s + t), which ensure that G has a Ks,t-factor. Our result extends the work of Zhao, who determined the minimum degree threshold which guarantees that a bipartite graph has a Ks,s-factor.