Graduation Year
2012
Document Type
Dissertation
Degree
Ph.D.
Degree Granting Department
Mathematics and Statistics
Major Professor
Brendan Nagle, Ph.D.
Committee Member
Jay Ligatti, Ph.D
Committee Member
Catherine Beneteau, Ph.D.
Committee Member
Brian W. Curtin, Ph.D.
Committee Member
Nat˘asa Jonoska, Ph.D.
Committee Member
Stephen Suen, Ph.D.
Keywords
extremal combinatorics, fractional packings, linear hypergraphs, regularity
Abstract
Let F0 be a fixed k-uniform hypergraph, and let H be a given k-uniform hypergraph on n vertices. An F0-packing of H is a family F of edge-disjoint copies of F0 which are subhypergraphs in H. Let nF0(H) denote the maximum size |F| of an F0-packing F of H. It is well-known that computing nF0(H) is NP-hard for nearly any choice of F0.
In this thesis, we consider the special case when F0 is a linear hypergraph, that is, when no two edges of F0 overlap in more than one vertex. We establish for z > 0 and n &ge n0(z) sufficiently large, an algorithm which, in time polynomial in n, constructs an F0-packing F of H of size |F| ≥ nF0(H) - znk.
A central direction in our proof uses so-called fractional F0-packings of H which are known to approximate nF0(H). The driving force of our argument, however, is the use and development of several tools within the theory of hypergraph regularity.
Scholar Commons Citation
Dizona, Jill, "On Algorithmic Fractional Packings of Hypergraphs" (2012). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/4029
