Tiling Tripartite Graphs with 3-Colorable Graphs: The Extreme Case.

There is a sufficiently large N∈hN<inline-graphic></inline-graphic> such that the following holds. If G is a tripartite graph with N vertices in each vertex class such that every vertex is adjacent to at least 2N/3+2h-1<inline-graphic></inline-graphic> vertices in each of the other classes, then G can be tiled perfectly by copies of Kh,h,h<inline-graphic></inline-graphic>. This extends work by Martin and Zhao (Electron J Combin 16(1):109, 2009) and also gives a sufficient condition for tiling by any fixed 3-colorable graph. Furthermore, we show that 2N/3+2h-1<inline-graphic></inline-graphic> in our result can not be replaced by 2N/3+h-2<inline-graphic></inline-graphic> and that if N is divisible by 6h, then we can replace it with the value 2N/3+h-1<inline-graphic></inline-graphic> and this is tight. [ABSTRACT FROM AUTHOR]