Extremal Problems for Forests in Graphs and Hypergraphs

Author

Omid Khormali

Year of Award

2019

Document Type

Dissertation

Degree Type

Doctor of Philosophy (PhD)

Degree Name

Mathematics

Department or School/College

Department of Mathematical Sciences

Committee Chair

Cory Palmer

Commitee Members

Mark Kayll, Brian Steele, Daniel Johnston, John Chandler

Keywords

Graph Forest, Hypergraph Forest, Turan Number

Abstract

The Turan number, ex_r(n; F), of an r-uniform hypergraph F is the maximum number of hyperedges in an n-vertex r-uniform hypergraph which does not contain F as a subhypergraph. Note that when r = 2, ex_r(n; F) = ex(n; F) which is the Turan number of graph F. We study.

Turan numbers in the degenerate case for graphs and hypergraphs; we focus on the case when F is a forest in graphs and hypergraph. In the first chapter we discuss the history of Turan numbers and give several classical results. In the second chapter, we examine the Turan number for forests with path components, forests of path and star components, and forests with all components of order 5. In the third chapter we determine the Turan number of an r-uniform "star forest" in various hypergraph settings.

Recommended Citation

Khormali, Omid, "Extremal Problems for Forests in Graphs and Hypergraphs" (2019). Graduate Student Theses, Dissertations, & Professional Papers. 11483.
https://scholarworks.umt.edu/etd/11483