Matching Items (20)
Filtering by
- Creators: Arizona State University
Description
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 $s$ vertices. The following theorem extends this result to directed graphs: If $D$ is a directed graph on $3k$ vertices with minimum total degree $delta(D)ge4k-1$ then $D$ can be partitioned into $k$ parts each of size $3$ so that all of parts contain a transitive triangle and $k-1$ of the parts also contain a cyclic triangle. The total degree of a vertex $v$ is the sum of $d^-(v)$ the in-degree and $d^+(v)$ the out-degree of $v$. Note that both orientations of $C_3$ are considered: the transitive triangle and the cyclic triangle. The theorem is best possible in that there are digraphs that meet the minimum degree requirement but have no cyclic triangle factor. The possibility of added a connectivity requirement to ensure a cycle triangle factor is also explored. Hajnal and Szemerédi proved that if $G$ is a graph on $sk$ vertices and $delta(G)ge(s-1)k$ then $G$ contains a $K_s$-factor. As a possible extension of this celebrated theorem to directed graphs it is proved that if $D$ is a directed graph on $sk$ vertices with $delta(D)ge2(s-1)k-1$ then $D$ contains $k$ disjoint transitive tournaments on $s$ vertices. We also discuss tiling directed graph with other tournaments. This study also explores minimum total degree conditions for perfect directed cycle tilings and sufficient semi-degree conditions for a directed graph to contain an anti-directed Hamilton cycle. The semi-degree of a vertex $v$ is $min{d^+(v), d^-(v)}$ and an anti-directed Hamilton cycle is a spanning cycle in which no pair of consecutive edges form a directed path.
ContributorsMolla, Theodore (Author) / Kierstead, Henry A (Thesis advisor) / Czygrinow, Andrzej (Committee member) / Fishel, Susanna (Committee member) / Hurlbert, Glenn (Committee member) / Spielberg, Jack (Committee member) / Arizona State University (Publisher)
Created2013
Description
Libby Larsen is one of the most performed and acclaimed composers today. She is a spirited, compelling, and sensitive composer whose music enhances the poetry of America's most prominent authors. Notable among her works are song cycles for soprano based on the poetry of female writers, among them novelist and poet Willa Cather (1873-1947). Larsen has produced two song cycles on works from Cather's substantial output of fiction: one based on Cather's short story, "Eric Hermannson's Soul," titled Margaret Songs: Three Songs from Willa Cather (1996); and later, My Antonia (2000), based on Cather's novel of the same title. In Margaret Songs, Cather's poetry and short stories--specifically the character of Margaret Elliot--combine with Larsen's unique compositional style to create a surprising collaboration. This study explores how Larsen in these songs delves into the emotional and psychological depths of Margaret's character, not fully formed by Cather. It is only through Larsen's music and Cather's poetry that Margaret's journey through self-discovery and love become fully realized. This song cycle is a glimpse through the eyes of two prominent female artists on the societal pressures placed upon Margaret's character, many of which still resonate with women in today's culture. This study examines the work Margaret Songs by discussing Willa Cather, her musical influences, and the conditions surrounding the writing of "Eric Hermannson's Soul." It looks also into Cather's influence on Libby Larsen and the commission leading to Margaret Songs. Finally, a description of the musical, dramatic, and textual content of the songs completes this interpretation of the interactions of Willa Cather, Libby Larsen, and the character of Margaret Elliot.
ContributorsMcLain, Christi Marie (Author) / FitzPatrick, Carole (Thesis advisor) / Dreyfoos, Dale (Committee member) / Holbrook, Amy (Committee member) / Ryan, Russell (Committee member) / Arizona State University (Publisher)
Created2013
Discovering Puerto Rican art song: a research project on four art song works by Héctor Campos Parsi
Description
Puerto Rico has produced many important composers who have contributed to the musical culture of the nation during the last 200 years. However, a considerable amount of their music has proven to be difficult to access and may contain numerous errors. This research project intends to contribute to the accessibility of such music and to encourage similar studies of Puerto Rican music. This study focuses on the music of Héctor Campos Parsi (1922-1998), one of the most prominent composers of the 20th century in Puerto Rico. After an overview of the historical background of music on the island and the biography of the composer, four works from his art song repertoire are given for detailed examination. A product of this study is the first corrected edition of his cycles Canciones de Cielo y Agua, Tres Poemas de Corretjer, Los Paréntesis, and the song Majestad Negra. These compositions date from 1947 to 1959, and reflect both the European and nationalistic writing styles of the composer during this time. Data for these corrections have been obtained from the composer's manuscripts, published and unpublished editions, and published recordings. The corrected scores are ready for publication and a compact disc of this repertoire, performed by soprano Melliangee Pérez and the author, has been recorded to bring to life these revisions. Despite the best intentions of the author, the various copyright issues have yet to be resolved. It is hoped that this document will provide the foundation for a resolution and that these important works will be available for public performance and study in the near future.
ContributorsRodríguez Morales, Luis F., 1980- (Author) / Campbell, Andrew (Thesis advisor) / Buck, Elizabeth (Committee member) / Holbrook, Amy (Committee member) / Kopta, Anne (Committee member) / Ryan, Russell (Committee member) / Arizona State University (Publisher)
Created2013
Description
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 $w^{14 \lg w}$ by Bosek and Krawczyk. This is improved to $w^{3+6.5 \lg w}$ by employing the First-Fit algorithm on a family of restricted posets (expanding on the work of Bosek and Krawczyk) . Namely, the family of ladder-free posets where the $m$-ladder is the transitive closure of the union of two incomparable chains $x_1\le\dots\le x_m$, $y_1\le\dots\le y_m$ and the set of comparabilities $\{x_1\le y_1,\dots, x_m\le y_m\}$. No upper bound on the number of colors needed to color a general on-line graph exists. To lay this fact plain, the performance of on-line coloring of trees is shown to be particularly problematic. There are trees that require $n$ colors to color on-line for any positive integer $n$. Furthermore, there are trees that usually require many colors to color on-line even if they are presented without any particular strategy. For restricted families of graphs, upper and lower bounds for the optimum number of colors needed to maintain an on-line coloring exist. In particular, circular arc graphs can be colored on-line using less than 8 times the optimum number from the static case. This follows from the work of Pemmaraju, Raman, and Varadarajan in on-line coloring of interval graphs.
ContributorsSmith, Matthew Earl (Author) / Kierstead, Henry A (Thesis advisor) / Colbourn, Charles (Committee member) / Czygrinow, Andrzej (Committee member) / Fishel, Susanna (Committee member) / Hurlbert, Glenn (Committee member) / Arizona State University (Publisher)
Created2012
Description
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 with the relationship between minimum degree conditions of a host graph G and the property that G contains a specified spanning subgraph (or class of subgraphs). The goal is to find the optimal minimum degree which guarantees the existence of a desired spanning subgraph. This goal is achieved in four different settings, with the main tools being Szemeredi's Regularity Lemma; the Blow-up Lemma of Komlos, Sarkozy, and Szemeredi; and some basic probabilistic techniques.
ContributorsDeBiasio, Louis (Author) / Kierstead, Henry A (Thesis advisor) / Czygrinow, Andrzej (Thesis advisor) / Hurlbert, Glenn (Committee member) / Kadell, Kevin (Committee member) / Fishel, Susanna (Committee member) / Arizona State University (Publisher)
Created2011
Description
Autism spectrum disorder (ASD) is a developmental neuropsychiatric condition with early childhood onset, thus most research has focused on characterizing brain function in young individuals. Little is understood about brain function differences in middle age and older adults with ASD, despite evidence of persistent and worsening cognitive symptoms. Functional Magnetic Resonance Imaging (MRI) in younger persons with ASD demonstrate that large-scale brain networks containing the prefrontal cortex are affected. A novel, threshold-selection-free graph theory metric is proposed as a more robust and sensitive method for tracking brain aging in ASD and is compared against five well-accepted graph theoretical analysis methods in older men with ASD and matched neurotypical (NT) participants. Participants were 27 men with ASD (52 +/- 8.4 years) and 21 NT men (49.7 +/- 6.5 years). Resting-state functional MRI (rs-fMRI) scans were collected for six minutes (repetition time=3s) with eyes closed. Data was preprocessed in SPM12, and Data Processing Assistant for Resting-State fMRI (DPARSF) was used to extract 116 regions-of-interest defined by the automated anatomical labeling (AAL) atlas. AAL regions were separated into six large-scale brain networks. This proposed metric is the slope of a monotonically decreasing convergence function (Integrated Persistent Feature, IPF; Slope of the IPF, SIP). Results were analyzed in SPSS using ANCOVA, with IQ as a covariate. A reduced SIP was in older men with ASD, compared to NT men, in the Default Mode Network [F(1,47)=6.48; p=0.02; 2=0.13] and Executive Network [F(1,47)=4.40; p=0.04; 2=0.09], a trend in the Fronto-Parietal Network [F(1,47)=3.36; p=0.07; 2=0.07]. There were no differences in the non-prefrontal networks (Sensory motor network, auditory network, and medial visual network). The only other graph theory metric to reach significance was network diameter in the Default Mode Network [F(1,47)=4.31; p=0.04; 2=0.09]; however, the effect size for the SIP was stronger. Modularity, Betti number, characteristic path length, and eigenvalue centrality were all non-significant. These results provide empirical evidence of decreased functional network integration in pre-frontal networks of older adults with ASD and propose a useful biomarker for tracking prognosis of aging adults with ASD to enable more informed treatment, support, and care methods for this growing population.
ContributorsCatchings, Michael Thomas (Author) / Braden, Brittany B (Thesis advisor) / Greger, Bradley (Thesis advisor) / Schaefer, Sydney (Committee member) / Arizona State University (Publisher)
Created2019
Description
Since the seminal work of Tur ́an, the forbidden subgraph problem has been among the central questions in extremal graph theory. Let ex(n;F) be the smallest number m such that any graph on n vertices with m edges contains F as a subgraph. Then the forbidden subgraph problem asks to find ex(n; F ) for various graphs F . The question can be further generalized by asking for the extreme values of other graph parameters like minimum degree, maximum degree, or connectivity. We call this type of question a Tura ́n-type problem. In this thesis, we will study Tura ́n-type problems and their variants for graphs and hypergraphs.
Chapter 2 contains a Tura ́n-type problem for cycles in dense graphs. The main result in this chapter gives a tight bound for the minimum degree of a graph which guarantees existence of disjoint cycles in the case of dense graphs. This, in particular, answers in the affirmative a question of Faudree, Gould, Jacobson and Magnant in the case of dense graphs.
In Chapter 3, similar problems for trees are investigated. Recently, Faudree, Gould, Jacobson and West studied the minimum degree conditions for the existence of certain spanning caterpillars. They proved certain bounds that guarantee existence of spanning caterpillars. The main result in Chapter 3 significantly improves their result and answers one of their questions by proving a tight minimum degree bound for the existence of such structures.
Chapter 4 includes another Tur ́an-type problem for loose paths of length three in a 3-graph. As a corollary, an upper bound for the multi-color Ramsey number for the loose path of length three in a 3-graph is achieved.
Chapter 2 contains a Tura ́n-type problem for cycles in dense graphs. The main result in this chapter gives a tight bound for the minimum degree of a graph which guarantees existence of disjoint cycles in the case of dense graphs. This, in particular, answers in the affirmative a question of Faudree, Gould, Jacobson and Magnant in the case of dense graphs.
In Chapter 3, similar problems for trees are investigated. Recently, Faudree, Gould, Jacobson and West studied the minimum degree conditions for the existence of certain spanning caterpillars. They proved certain bounds that guarantee existence of spanning caterpillars. The main result in Chapter 3 significantly improves their result and answers one of their questions by proving a tight minimum degree bound for the existence of such structures.
Chapter 4 includes another Tur ́an-type problem for loose paths of length three in a 3-graph. As a corollary, an upper bound for the multi-color Ramsey number for the loose path of length three in a 3-graph is achieved.
ContributorsYie, Jangwon (Author) / Czygrinow, Andrzej (Thesis advisor) / Kierstead, Henry (Committee member) / Colbourn, Charles (Committee member) / Fishel, Susanna (Committee member) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2018
Description
Measuring node centrality is a critical common denominator behind many important graph mining tasks. While the existing literature offers a wealth of different node centrality measures, it remains a daunting task on how to intervene the node centrality in a desired way. In this thesis, we study the problem of minimizing the centrality of one or more target nodes by edge operation. The heart of the proposed method is an accurate and efficient algorithm to estimate the impact of edge deletion on the spectrum of the underlying network, based on the observation that the edge deletion is essentially a local, sparse perturbation to the original network. Extensive experiments are conducted on a diverse set of real networks to demonstrate the effectiveness, efficiency and scalability of our approach. In particular, it is average of 260.95%, in terms of minimizing eigen-centrality, better than the standard matrix-perturbation based algorithm, with lower time complexity.
ContributorsPeng, Ruiyue (Author) / Tong, Hanghang (Thesis advisor) / He, Jingrui (Committee member) / Davulcu, Hasan (Committee member) / Arizona State University (Publisher)
Created2016
Description
Higher-rank graphs, or k-graphs, are higher-dimensional analogues of directed graphs, and as with ordinary directed graphs, there are various C*-algebraic objects that can be associated with them. This thesis adopts a functorial approach to study the relationship between k-graphs and their associated C*-algebras. In particular, two functors are given between appropriate categories of higher-rank graphs and the category of C*-algebras, one for Toeplitz algebras and one for Cuntz-Krieger algebras. Additionally, the Cayley graphs of finitely generated groups are used to define a class of k-graphs, and a functor is then given from a category of finitely generated groups to the category of C*-algebras. Finally, functoriality is investigated for product systems of C*-correspondences associated to k-graphs. Additional results concerning the structural consequences of functoriality, properties of the functors, and combinatorial aspects of k-graphs are also included throughout.
ContributorsEikenberry, Keenan (Author) / Quigg, John (Thesis advisor) / Kaliszewski, Steven (Thesis advisor) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2016
Description
Graph coloring is about allocating resources that can be shared except where there are certain pairwise conflicts between recipients. The simplest coloring algorithm that attempts to conserve resources is called first fit. Interval graphs are used in models for scheduling (in computer science and operations research) and in biochemistry for one-dimensional molecules such as genetic material. It is not known precisely how much waste in the worst case is due to the first-fit algorithm for coloring interval graphs. However, after decades of research the range is narrow. Kierstead proved that the performance ratio R is at most 40. Pemmaraju, Raman, and Varadarajan proved that R is at most 10. This can be improved to 8. Witsenhausen, and independently Chrobak and Slusarek, proved that R is at least 4. Slusarek improved this to 4.45. Kierstead and Trotter extended the method of Chrobak and Slusarek to one good for a lower bound of 4.99999 or so. The method relies on number sequences with a certain property of order. It is shown here that each sequence considered in the construction satisfies a linear recurrence; that R is at least 5; that the Fibonacci sequence is in some sense minimally useless for the construction; and that the Fibonacci sequence is a point of accumulation in some space for the useful sequences of the construction. Limitations of all earlier constructions are revealed.
ContributorsSmith, David A. (Author) / Kierstead, Henry A. (Thesis advisor) / Czygrinow, Andrzej (Committee member) / Gelb, Anne (Committee member) / Hurlbert, Glenn H. (Committee member) / Kadell, Kevin W. J. (Committee member) / Arizona State University (Publisher)
Created2010