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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
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
ContributorsShi, Ge (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-25
ContributorsShatuho, Kristina (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-27
ContributorsCarlisi, Daniel (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-07
Description
Yannis Constantinidis was the last of the handful of composers referred to collectively as the Greek National School. The members of this group strove to create a distinctive national style for Greece, founded upon a synthesis of Western compositional idioms with melodic, rhyhmic, and modal features of their local folk traditions. Constantinidis particularly looked to the folk melodies of his native Asia Minor and the nearby Dodecanese Islands. His musical output includes operettas, musical comedies, orchestral works, chamber and vocal music, and much piano music, all of which draws upon folk repertories for thematic material. The present essay examines how he incorporates this thematic material in his piano compositions, written between 1943 and 1971, with a special focus on the 22 Songs and Dances from the Dodecanese. In general, Constantinidis's pianistic style is expressed through miniature pieces in which the folk tunes are presented mostly intact, but embedded in accompaniment based in early twentieth-century modal harmony. Following the dictates of the founding members of the Greek National School, Manolis Kalomiris and Georgios Lambelet, the modal basis of his harmonic vocabulary is firmly rooted in the characteristics of the most common modes of Greek folk music. A close study of his 22 Songs and Dances from the Dodecanese not only offers a valuable insight into his harmonic imagination, but also demonstrates how he subtly adapts his source melodies. This work also reveals his care in creating a musical expression of the words of the original folk songs, even in purely instrumental compositon.
ContributorsSavvidou, Dina (Author) / Hamilton, Robert (Thesis advisor) / Little, Bliss (Committee member) / Meir, Baruch (Committee member) / Thompson, Janice M (Committee member) / Arizona State University (Publisher)
Created2011
Description
This paper describes six representative works by twentieth-century Chinese composers: Jian-Zhong Wang, Er-Yao Lin, Yi-Qiang Sun, Pei-Xun Chen, Ying-Hai Li, and Yi Chen, which are recorded by the author on the CD. The six pieces selected for the CD all exemplify traits of Nationalism, with or without Western influences. Of the six works on the CD, two are transcriptions of the Han Chinese folk-like songs, one is a composition in the style of the Uyghur folk music, two are transcriptions of traditional Chinese instrumental music dating back to the eighteenth century, and one is an original composition in a contemporary style using folk materials. Two of the composers, who studied in the United States, were strongly influenced by Western compositional style. The other four, who did not study abroad, retained traditional Chinese style in their compositions. The pianistic level of difficulty in these six pieces varies from intermediate to advanced level. This paper includes biographical information for the six composers, background information on the compositions, and a brief analysis of each work. The author was exposed to these six pieces growing up, always believing that they are beautiful and deserve to be appreciated. When the author came to the United States for her studies, she realized that Chinese compositions, including these six pieces, were not sufficiently known to her peers. This recording and paper are offered in the hopes of promoting a wider familiarity with Chinese music and culture.
ContributorsLuo, Yali, D.M.A (Author) / Hamilton, Robert (Thesis advisor) / Campbell, Andrew (Committee member) / Pagano, Caio (Committee member) / Cosand, Walter (Committee member) / Rogers, Rodney (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
The purpose of this project was to examine the lives and solo piano works of four members of the early generation of female composers in Taiwan. These four women were born between 1950 and 1960, began to appear on the Taiwanese musical scene after 1980, and were still active as composers at the time of this study. They include Fan-Ling Su (b. 1955), Hwei-Lee Chang (b. 1956), Shyh-Ji Pan-Chew (b. 1957), and Kwang-I Ying (b. 1960). Detailed biographical information on the four composers is presented and discussed. In addition, the musical form and features of all solo piano works at all levels by the four composers are analyzed, and the musical characteristics of each composer's work are discussed. The biography of a fifth composer, Wei-Ho Dai (b. 1950), is also discussed but is placed in the Appendices because her piano music could not be located. This research paper is presented in six chapters: (1) Prologue; the life and music of (2) Fan-Ling Su, (3) Hwei-Lee Chang, (4) Shyh-Ji Pan-Chew, and (5) Kwang-I Ying; and (6) Conclusion. The Prologue provides an overview of the development of Western classical music in Taiwan, a review of extant literature on the selected composers and their music, and the development of piano music in Taiwan. The Conclusion is comprised of comparisons of the four composers' music, including their personal interests and preferences as exhibited in their music. For example, all of the composers have used atonality in their music. Two of the composers, Fan-Ling Su and Kwang-I Ying, openly apply Chinese elements in their piano works, while Hwei-Lee Chang tries to avoid direct use of the Chinese pentatonic scale. The piano works of Hwei-Lee Chang and Shyh-Ji Pan-Chew are chromatic and atonal, and show an economical usage of material. Biographical information on Wei-Ho Dai and an overview of Taiwanese history are presented in the Appendices.
ContributorsWang, Jinding (Author) / Pagano, Caio (Thesis advisor) / Campbell, Andrew (Committee member) / Humphreys, Jere T. (Committee member) / Meyer-Thompson, Janice (Committee member) / Norton, Kay (Committee member) / Arizona State University (Publisher)
Created2011
ContributorsShi, Zhan (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-26