Date of Award

Summer 8-1-2011

Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

First Advisor

Yi Zhao


We consider tiling problems for graphs and hypergraphs. For two graphs and , an -tiling of is a subgraph of consisting of only vertex disjoint copies of . By using the absorbing method, we give a short proof that in a balanced tripartite graph , if every vertex is adjacent to of the vertices in each of the other vertex partitions, then has a -tiling. Previously, Magyar and Martin [11] proved the same result (without ) by using the Regularity Lemma.

In a 3-uniform hypergraph , let denote the minimum number of edges that contain for all pairs of vertices. We show that if , there exists a -tiling that misses at most vertices of . On the other hand, we show that there exist hypergraphs such that and does not have a perfect -tiling. These extend the results of Pikhurko [12] on -tilings.

Included in

Mathematics Commons