Note on bipartite graph tilings

TL;DR

This paper determines the minimum degree conditions needed for bipartite graphs to contain a complete bipartite subgraph factor, extending previous results to more general bipartite subgraphs.

Contribution

It provides an exact minimum degree threshold for bipartite graphs to contain a K_{s,t}-factor, generalizing prior work on K_{s,s}-factors.

Findings

Exact minimum degree condition for large n

Extension of Zhao's result to K_{s,t}-factors

Conditions ensure bipartite graph tilings with K_{s,t}

Abstract

Let s<t be two fixed positive integers. We study what are the minimum degree conditions for a bipartite graph G, with both color classes of size n=k(s+t), which ensure that G has a K_{s,t}-factor. Exact result for large n is given. Our result extends the work of Zhao, who determined the minimum degree threshold which guarantees that a bipartite graph has a K_{s,s}-factor.