Date of Award
Summer 8-1-2011
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
First Advisor
Yi Zhao
Abstract
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.
DOI
https://doi.org/10.57709/2102205
Recommended Citation
Lightcap, Andrew, "Minimum Degree Conditions for Tilings in Graphs and Hypergraphs." Thesis, Georgia State University, 2011.
doi: https://doi.org/10.57709/2102205