## ASU Electronic Theses and Dissertations

This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.

In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.

Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.

- Czygrinow, Andrzej
- 14 Arizona State University
- 12 Fishel, Susanna
- 7 Colbourn, Charles
- 5 Hurlbert, Glenn
- 5 Kierstead, Henry
- 4 Jones, John
- more
- 3 Kierstead, Henry A
- 3 Spielberg, John
- 2 Childress, Nancy
- 1 AL-SULEIMAN, SULTAN
- 1 Bremner, Andrew
- 1 Colbourn, Charles J.
- 1 Debiasio, Louis
- 1 Gelb, Anne
- 1 Horan, Victoria E.
- 1 Hurlbert, Glenn H
- 1 Hurlbert, Glenn H.
- 1 Kadell, Kevin
- 1 Kadell, Kevin W. J.
- 1 Kamat, Vikram Mahendra
- 1 Kierstead, Hal A
- 1 Kierstead, Henry A.
- 1 Kim, Younghwan
- 1 Molla, Theodore
- 1 Nelson, Luke Edwin
- 1 Oursler, Roy
- 1 Paupert, Julien
- 1 Rabern, Landon
- 1 Richa, Andrea W.
- 1 Sarkar, Kaushik
- 1 Sen, Arunabha
- 1 Smith, David A.
- 1 Smith, Matthew Earl
- 1 Spielberg, Jack
- 1 Syrotiuk, Violet R.
- 1 Treat, Kevin
- 1 Yie, Jangwon

- 14 English

- 14 Public

- Mathematics
- 2 Maximal Chains
- 2 Tamari Lattices
- 1 Borodin-Kostochka
- 1 Brooks
- 1 Cambrian Lattices
- 1 Catalan lattice
- more
- 1 Circular arc graph
- 1 Combinatorics
- 1 Computer Science
- 1 Computer science
- 1 Degree
- 1 Directed Graphs
- 1 Enumeration
- 1 Extremal Graph Theory
- 1 First-Fit
- 1 Graph
- 1 Graph Theory
- 1 Gray codes
- 1 Higher Stasheff-Tamari order
- 1 Hypergraph
- 1 Lattices
- 1 Loose Cycle
- 1 On-line chain partition
- 1 On-line graph coloring
- 1 Partially ordered set
- 1 Rainbow Cycle
- 1 Ramsey Number
- 1 Tamari lattice
- 1 Theoretical mathematics
- 1 Tiling
- 1 Tree
- 1 Turan Number
- 1 affine permutation
- 1 cd-index
- 1 chordal graphs
- 1 chvatal's conjecture
- 1 clique
- 1 coloring
- 1 combinatorial design
- 1 covering arrays
- 1 covering perfect hash families
- 1 cross-intersecting families
- 1 cyclic sieving phenomenon
- 1 first-fit
- 1 flag enumeration
- 1 graph coloring
- 1 independent sets
- 1 intersecting families
- 1 interval graphs
- 1 m-eralized Cambrian Lattices
- 1 matchings
- 1 maximum degree
- 1 orthogonal arrays
- 1 overlap cycles
- 1 partial covering arrays
- 1 software interaction testing
- 1 stability analysis
- 1 the uncrossing partial order
- 1 universal cycles

- Microfluidic Models of Tumor-Stroma Interactions to Study the Interplay of Cancer Cells with their Surrounding Microenvironment
- Ain't She Sweet: A Critical Choreographic Study of Identity & Intersectionality
- Suppositions for Desert Modernism: An Architectural Framework Informed by Climate, Natural Light, and Topography
- Concurrent reduction of trichloroethylene and perchlorate in continuous flow-through soil columns
- Design and Fabrication of Fabric ReinforcedTextile Actuators forSoft Robotic Graspers

Every graph can be colored with one more color than its maximum degree. A well-known theorem of Brooks gives the precise conditions under which a graph can be colored with maximum degree colors. It is natural to ask for the required conditions on a graph to color with one less color than the maximum degree; in 1977 Borodin and Kostochka conjectured a solution for graphs with maximum degree at least 9: as long as the graph doesn't contain a maximum-degree-sized clique, it can be colored with one fewer than the maximum degree colors. This study attacks the conjecture on multiple ...

- Contributors
- Rabern, Landon, Kierstead, Henry, Colbourn, Charles, et al.
- Created Date
- 2013

Modern software and hardware systems are composed of a large number of components. Often different components of a system interact with each other in unforeseen and undesired ways to cause failures. Covering arrays are a useful mathematical tool for testing all possible t-way interactions among the components of a system. The two major issues concerning covering arrays are explicit construction of a covering array, and exact or approximate determination of the covering array number---the minimum size of a covering array. Although these problems have been investigated extensively for the last couple of decades, in this thesis we present significant improvements ...

- Contributors
- Sarkar, Kaushik, Colbourn, Charles J., Czygrinow, Andrzej, et al.
- Created Date
- 2016

The primary focus of this dissertation lies in extremal combinatorics, in particular intersection theorems in finite set theory. A seminal result in the area is the theorem of Erdos, Ko and Rado which finds the upper bound on the size of an intersecting family of subsets of an n-element set and characterizes the structure of families which attain this upper bound. A major portion of this dissertation focuses on a recent generalization of the Erdos--Ko--Rado theorem which considers intersecting families of independent sets in graphs. An intersection theorem is proved for a large class of graphs, namely chordal graphs which ...

- Contributors
- Kamat, Vikram Mahendra, Hurlbert, Glenn, Colbourn, Charles, et al.
- Created Date
- 2011

Gray codes are perhaps the best known structures for listing sequences of combinatorial objects, such as binary strings. Simply defined as a minimal change listing, Gray codes vary greatly both in structure and in the types of objects that they list. More specific types of Gray codes are universal cycles and overlap sequences. Universal cycles are Gray codes on a set of strings of length n in which the first n-1 letters of one object are the same as the last n-1 letters of its predecessor in the listing. Overlap sequences allow this overlap to vary between 1 and n-1. ...

- Contributors
- Horan, Victoria E., Hurlbert, Glenn H, Czygrinow, Andrzej, et al.
- Created Date
- 2012

The Tamari lattice T(n) was originally defined on bracketings of a set of n+1 objects, with a cover relation based on the associativity rule in one direction. Since then it has been studied in various areas of mathematics including cluster algebras, discrete geometry, algebraic combinatorics, and Catalan theory. Although in several related lattices the number of maximal chains is known, the enumeration of these chains in Tamari lattices is still an open problem. This dissertation defines a partially-ordered set on equivalence classes of certain saturated chains of T(n) called the Tamari Block poset, TB(lambda). It further proves TB(lambda) is a ...

- Contributors
- Treat, Kevin, Fishel, Susanna, Czygrinow, Andrzej, et al.
- Created Date
- 2016

Extremal graph theory results often provide minimum degree conditions which guarantee a copy of one graph exists within another. A perfect $F$-tiling of a graph $G$ is a collection $\mathcal{F}$ of subgraphs of $G$ such that every element of $\mathcal{F}$ is isomorphic to $F$ and such that every vertex in $G$ is in exactly one element of $\mathcal{F}$. Let $C^{3}_{t}$ denote the loose cycle on $t = 2s$ vertices, the $3$-uniform hypergraph obtained by replacing the edges $e = \{u, v\}$ of a graph cycle $C$ on $s$ vertices with edge triples $\{u, x_e, v\}$, where $x_e$ is uniquely assigned ...

- Contributors
- Oursler, Roy, Czygrinow, Andrzej, Kierstead, Hal A, et al.
- Created Date
- 2019

The uncrossing partially ordered set $P_n$ is defined on the set of matchings on $2n$ points on a circle represented with wires. The order relation is $\tau'\leq \tau$ in $P_n$ if and only if $\tau'$ is obtained by resolving a crossing of $\tau$. %This partial order has been studied by Alman-Lian-Tran, Huang-Wen-Xie, Kenyon, and Lam. %The posets $P_n$ emerged from studies of circular planar electrical networks. Circular planar electrical networks are finite weighted undirected graphs embedded into a disk, with boundary vertices and interior vertices. By Curtis-Ingerman-Morrow and de Verdi\`ere-Gitler-Vertigan, the electrical networks can be encoded with response matrices. By ...

- Contributors
- Kim, Younghwan, Fishel, Susanna, Bremner, Andrew, et al.
- Created Date
- 2018

A tiling is a collection of vertex disjoint subgraphs called tiles. If the tiles are all isomorphic to a graph $H$ then the tiling is an $H$-tiling. If a graph $G$ has an $H$-tiling which covers all of the vertices of $G$ then the $H$-tiling is a perfect $H$-tiling or an $H$-factor. A goal of this study is to extend theorems on sufficient minimum degree conditions for perfect tilings in graphs to directed graphs. Corrádi and Hajnal proved that every graph $G$ on $3k$ vertices with minimum degree $delta(G)ge2k$ has a $K_3$-factor, where $K_s$ is the complete graph on $s$ ...

- Contributors
- Molla, Theodore, Kierstead, Henry A, Czygrinow, Andrzej, et al.
- Created Date
- 2013

A central concept of combinatorics is partitioning structures with given constraints. Partitions of on-line posets and on-line graphs, which are dynamic versions of the more familiar static structures posets and graphs, are examined. In the on-line setting, vertices are continually added to a poset or graph while a chain partition or coloring (respectively) is maintained. %The optima of the static cases cannot be achieved in the on-line setting. Both upper and lower bounds for the optimum of the number of chains needed to partition a width $w$ on-line poset exist. Kierstead's upper bound of $\frac{5^w-1}{4}$ was improved to $w^{14 \lg ...

- Contributors
- Smith, Matthew Earl, Kierstead, Henry A, Colbourn, Charles, et al.
- Created Date
- 2012

In a large network (graph) it would be desirable to guarantee the existence of some local property based only on global knowledge of the network. Consider the following classical example: how many connections are necessary to guarantee that the network contains three nodes which are pairwise adjacent? It turns out that more than n^2/4 connections are needed, and no smaller number will suffice in general. Problems of this type fall into the category of ``extremal graph theory.'' Generally speaking, extremal graph theory is the study of how global parameters of a graph are related to local properties. This dissertation deals ...

- Contributors
- Debiasio, Louis, Kierstead, Henry A, Czygrinow, Andrzej, et al.
- Created Date
- 2011