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Ruihong Chang, violin

ContributorsChang, Ruihong (Performer) / ASU Library. Music Library (Publisher)

Created2018-03-29

Optimal degree conditions for spanning subgraphs

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…

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

Paul Schoenfeld and h\s Four souvenirs for violin and piano (1990)

Description

Four Souvenirs for Violin and Piano was composed by Paul Schoenfeld (b.1947) in 1990 as a showpiece, spotlighting the virtuosity of both the violin and piano in equal measure. Each movement is a modern interpretation of a folk or popular genre, re- envisioned over intricate jazz harmonies and rhythms. The…

Four Souvenirs for Violin and Piano was composed by Paul Schoenfeld (b.1947) in 1990 as a showpiece, spotlighting the virtuosity of both the violin and piano in equal measure. Each movement is a modern interpretation of a folk or popular genre, re- envisioned over intricate jazz harmonies and rhythms. The work was commissioned by violinist Lev Polyakin, who specifically requested some short pieces that could be performed in a local jazz establishment named Night Town in Cleveland, Ohio. The result is a work that is approximately fifteen minutes in length. Schoenfeld is a respected composer in the contemporary classical music community, whose Café Music (1986) for piano trio has recently become a staple of the standard chamber music repertoire. Many of his other works, however, remain in relative obscurity. It is the focus of this document to shed light on at least one other notable composition; Four Souvenirs for Violin and Piano. Among the topics to be discussed regarding this piece are a brief history behind the genesis of this composition, a structural summary of the entire work and each of its movements, and an appended practice guide based on interview and coaching sessions with the composer himself. With this project, I hope to provide a better understanding and appreciation of this work.

ContributorsJanczyk, Kristie Annette (Author) / Ryan, Russell (Thesis advisor) / Campbell, Andrew (Committee member) / Norton, Kay (Committee member) / Arizona State University (Publisher)

Created2015

Some Turán-type problems in extremal graph theory

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…

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.

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