Degree Granting Department
Mathematics and Statistics
Brendan Nagle, Ph.D.
Jay Ligatti, Ph.D
Catherine Beneteau, Ph.D.
Brian W. Curtin, Ph.D.
Nat˘asa Jonoska, Ph.D.
Stephen Suen, Ph.D.
extremal combinatorics, fractional packings, linear hypergraphs, regularity
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.