Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Articles 1 - 30 of 67

Full-Text Articles in Physical Sciences and Mathematics

Computational Studies Of The Properties Of Copper Oxide Clusters And The Reactions Of Phenol And Chlorinated Phenols With Copper Oxide Clusters, Gyun-Tack Bae Jan 2009

Computational Studies Of The Properties Of Copper Oxide Clusters And The Reactions Of Phenol And Chlorinated Phenols With Copper Oxide Clusters, Gyun-Tack Bae

LSU Doctoral Dissertations

We used ab initio simulations and calculations to study the structures and stabilities of copper oxide clusters, CunOn (n=1-8) and CuOn (n=1-6). The lowest energy structures of neutral and charged copper oxide clusters were determined using primarily the B3LYP/LANL2DZ model chemistry. In CunOn clusters with n=1-8, a transition from planar to nonplanar geometries occurs at n=4. In CuOn clusters with n=1-6, all geometries of neutral, positively, and negatively charged clusters are planar or near planar structures. Selected electronic properties, including binding energies, ionization energies, and electronic affinities, were calculated and examined as a function of n. Stabilities were examined by …


A Multi-Proxy Approach To Investigating The Latest Holocene (~4,500 Yrs. Bp) Vegetational History Of Catahoula Lake, Louisiana, Rebecca Ann Tedford Jan 2009

A Multi-Proxy Approach To Investigating The Latest Holocene (~4,500 Yrs. Bp) Vegetational History Of Catahoula Lake, Louisiana, Rebecca Ann Tedford

LSU Doctoral Dissertations

A multi-proxy investigation of sediments examined from Catahoula Lake, Louisiana has provided a record of late-Holocene vegetational changes, related to both hydrology and climate. This study integrates data from phytoliths, pollen, stable isotopes, magnetic susceptibility, and core sediment analysis. A modern phytolith analog assessed the phytoliths production in local plants and their modern soil sample distribution within the established lake vegetation zones. Fifty of the 76 species produced both distinctive and redundant phytoliths. The modern soil sample database indicates that phytoliths produced from both monocotyledon and dicotlyledon plant groups prove useful in distinguishing between forest and grassland communities and identifying …


Bottom Boundary Layer Physics And Sediment Transport Along A Transgressive Sand Body, Ship Shoal, South-Central Louisiana: Implications For Fluvial Sediments And Winter Storms, Daijiro Kobashi Jan 2009

Bottom Boundary Layer Physics And Sediment Transport Along A Transgressive Sand Body, Ship Shoal, South-Central Louisiana: Implications For Fluvial Sediments And Winter Storms, Daijiro Kobashi

LSU Doctoral Dissertations

Ship Shoal, a shore-parallel sand body, was recently recognized as having a unique physical and biological environment and also as a potential sand resource for coastal restoration in coastal Louisiana. Little is known regarding such dynamics, in concert with fluvial sediments and winter storms, influenced in unique ecosystems, and likely in future potential sand mining. This dissertation addresses such the morphodynamics and sedimentary processes and their implications for the mining from the shoal using field measurements and numerical modeling studies. During the winter-spring season, fluvial sediment plumes shifted from the prevailing west to southeast during the post-frontal phases, resulted in …


Proxy Records Of Paleohurricanes For The Western And Southern Caribbean, Terrence Allen Mccloskey Jan 2009

Proxy Records Of Paleohurricanes For The Western And Southern Caribbean, Terrence Allen Mccloskey

LSU Doctoral Dissertations

This dissertation evaluates the hypothesis that hurricane activity levels in the North Atlantic during the late Holocene have been driven by latitudinal movements of the North Atlantic circulation system. Multi-millennial sedimentary proxy records, based on the occurrence of overwash clastic layers, provide clear evidence of abruptly alternating periods of hurricane landfall frequency for Nicaragua and Belize. Three Belizean transects exhibit an Active period (hyperactivity) occurring from ~2000-6000 cal yr BP, although dating is inconsistent across the transects. An Active period covering the last 500 years is found at one location. The Nicaraguan record, derived from three transects covering >90 km …


Sedimentation On A Mixed Siliciclastic/Carbonate Continental Margin Over Decadal To Millennial Timescales: Gulf Of Papua, Zahid Muhammad Jan 2009

Sedimentation On A Mixed Siliciclastic/Carbonate Continental Margin Over Decadal To Millennial Timescales: Gulf Of Papua, Zahid Muhammad

LSU Doctoral Dissertations

Sediments from the Gulf of Papua were examined to estimate particle flux and sediment mass accumulation rates on multiple timescales. Patterns of sediment mass accumulation and inventory-derived 210Pb fluxes display regional variations, decreasing seaward, and along isobaths seaward from the northeastern shelf edge. The amount of terrigenous sediment load being discharged annually from the shelf and accumulating in Pandora Trough is approximately 7-14×106 tonnes. The existence of possible turbidity-current transport and deposition have been documented in deeper parts of the Gulf of Papua. High excess 210Pb fluxes estimated from seabed inventories at the shelf edge and upper slope are consistent …


Testing Of Gdcl3 Doping In Water Cherenkov Antineutrino Detectors, William Fitzgerald Coleman Jan 2009

Testing Of Gdcl3 Doping In Water Cherenkov Antineutrino Detectors, William Fitzgerald Coleman

LSU Doctoral Dissertations

Improved neutron and neutrino detection using water Cherenkov detectors loaded with gadolinium has been proposed for potential application in both large and small volume detectors. In this thesis, work performed to determine the effect on transparency resulting from use of GdCl3 in stainless steel constructed water Cherenkov detectors is presented. In addition, results of an experiment performed using a small volume water Cherenkov de- tector are reported. This was the first use of gadolinium loaded water to detect reactor antineutrinos.


Derivatization Of Porphyrins For Dna And Metal Ion Binding, Especially By Employing Secondary Sulfonamide Links, Janet Manono Jan 2009

Derivatization Of Porphyrins For Dna And Metal Ion Binding, Especially By Employing Secondary Sulfonamide Links, Janet Manono

LSU Doctoral Dissertations

Porphyrins are of exceptional importance in nature, science and technology: For instance, as ligands for metals in supramolecular synthesis, as photosenstizers in photodynamic therapy (PDT), and as building blocks for electronic devices. In addition to their application in cancer therapy, porphyrin species also exhibit antiviral activity. New meso-tetraarylporphyrins (TArP, Ar = -C6H4-) of the general formula, T(R1R2NSO2Ar)P, with R1 = N-py-n-CH2 (n = 2, 3 or 4) or SO3- and R2 = H or CH3 were synthesized. These groups were linked to the …


Fabrication Of Nanostructured Surfaces With Well-Defined Chemistry Using Particle Lithography, Jie-Ren Li Jan 2009

Fabrication Of Nanostructured Surfaces With Well-Defined Chemistry Using Particle Lithography, Jie-Ren Li

LSU Doctoral Dissertations

Natural self-assembly processes provide nanofabrication capabilities for designing surfaces with nanoscale control of surface chemistry and relative orientation of the nanomaterials on the surfaces. Particle lithography was used to produce periodic arrays of protein nanostructures. Monodisperse mesoparticles can be applied to rapidly prepare millions of uniform protein nanostructures on flat surfaces using the conventional benchtop chemistry steps of mixing, centrifuging, evaporation and drying. Nanopatterns of bovine serum albumin and staphylococcal protein A were produced with particle lithography. The immobilized proteins remain attached to the surface and form nanopatterns over micron areas corresponding to the thickness of a single layer of …


Barrier Island Migration Over A Consolidating Substrate, Julie Dean Rosati Jan 2009

Barrier Island Migration Over A Consolidating Substrate, Julie Dean Rosati

LSU Doctoral Dissertations

Barrier islands that overlie a compressible substrate load and consolidate the underlying subsurface. Through time, the elevation and aerial extent of these islands are reduced, making them more susceptible to inundation and overwash. Sand washed over the island and onto back-barrier marsh or into the bay or estuary begins the consolidation process on a previously non-loaded substrate, with time-dependent consolidation a function of the magnitude of the load, duration of load, and characteristics of the substrate. The result is an increase in the overwash, migration, breaching, and segmentation of these islands. This research determined the degree to which consolidation affects …


Platforms And Protocols For The Multidimensional Microchip Electrophoretic Analysis Of Complex Proteomes, John K. Osiri Jan 2009

Platforms And Protocols For The Multidimensional Microchip Electrophoretic Analysis Of Complex Proteomes, John K. Osiri

LSU Doctoral Dissertations

The need for rapid, portable and high-throughput systems in proteomics is now prevalent because of demands for generating new protein-based disease biomarkers. However, 2-D protein profile patterns are lending themselves as potential diagnostic tools for biomarker discovery. It is difficult to identify protein biomarkers which are low abundant in the presence of highly abundant proteins, especially in complex biological samples like serum. Protein profiles from 2-D separation of the protein content of cells or body fluids, which are unique to certain physiological or pathological states, are currently available on internet databases. In this work, we demonstrate the ability to separate …


Studies Of Homogeneous Dirhodium Catalyst System, Catherine L. Thomas Alexander Jan 2009

Studies Of Homogeneous Dirhodium Catalyst System, Catherine L. Thomas Alexander

LSU Doctoral Dissertations

Hydroformylation studies were conducted to investigate the effects of various H&sub2;/CO ratios on rac-[Rh&sub2;H&sub2;(μ-CO)&sub2;(et,ph-P4)]²+;, a dirhodium tetraphosphine catalyst system. Similar experiments were also conducted with monometallic catalysts based on BISBI, NAPHOS, and Xantphos, some of the best bisphosphine ligands for hydroformylation catalysis. This was due to the lack of information in literature on the effects of variable ratios and pressures on activities and selectivities of catalysts that contain bisphosphine ligands, and these studies were also used as a basis of comparison for the dirhodium system. Results indicate that the dirhodium system is more efficient with higher H&sub2;/CO ratios (2:1, 90 …


Amyloid Aggregation-Mitigating Peptides As Potential Alzheimer's Drugs, Cyrus Kipkurui Bett Jan 2009

Amyloid Aggregation-Mitigating Peptides As Potential Alzheimer's Drugs, Cyrus Kipkurui Bett

LSU Doctoral Dissertations

Neuronal cytotoxicity observed in Alzheimer¡¦s disease (AD) is linked to the aggregation of £]-amyloid peptide (A£]) into toxic forms. Increasing evidence points to oligomeric species as the neurotoxic species compared to fibrils; disruption or inhibition of A£]ƒnself-assembly into oligomeric or fibrillar forms remains a viable therapeutic strategy to reduce A£] neurotoxicity. Amyloid aggregation mitigating peptides (AAMPs) were designed based on the A£]ƒn¡§hydrophobic core¡¨ A£]17-20, with C£\,£\-disubstituted amino acidsƒnƒv£\£\AAs) added into this core as disrupting agents. The number, distribution, and side chain functionality of £\£\AAs incorporated into the mitigator sequence was found influences the resultant aggregate morphology as indicated by ex-situ …


Single-Molecule Detection Of Unique Genome Signatures: Applications In Molecular Diagnostics And Homeland Security, Jason M. Emory Jan 2009

Single-Molecule Detection Of Unique Genome Signatures: Applications In Molecular Diagnostics And Homeland Security, Jason M. Emory

LSU Doctoral Dissertations

Single-molecule detection (SMD) offers an attractive approach for identifying the presence of certain markers that can be used for in vitro molecular diagnostics in a near real-time format. The ability to eliminate sample processing steps afforded by the ultra-high sensitivity associated with SMD yields an increased sampling pipeline. When SMD and microfluidics are used in conjunction with nucleic acid-based assays such as the ligase detection reaction coupled with single-pair fluorescent resonance energy transfer (LDR-spFRET), complete molecular profiling and screening of certain cancers, pathogenic bacteria, and other biomarkers becomes possible at remarkable speeds and sensitivities with high specificity. The merging of …


Anthropogenic And Natural Perturbations On Lower Barataria Bay, Louisiana: Detecting Responses Of Marsh-Edge Fishes And Decapod Crustaceans, Agatha-Marie Fuller Roth Jan 2009

Anthropogenic And Natural Perturbations On Lower Barataria Bay, Louisiana: Detecting Responses Of Marsh-Edge Fishes And Decapod Crustaceans, Agatha-Marie Fuller Roth

LSU Doctoral Dissertations

Barataria Bay, Louisiana is a dynamic estuary with ongoing disturbances that is in need of restoration. Development and validation of a lower Barataria Bay index of biotic integrity (IBI) for the summer season was the focus of my research. This IBI was created using 2005 data and evaluated with 2006 and 2007 data to demonstrate the feasibility of this approach in coastal Louisiana. The IBI successfully distinguished sites with differing levels of degradation using nine fish metrics. While pursuing this effort, two serendipitous events occurred when an oil spill then a hurricane impacted the study area. This gave me opportunities …


Local Behavior Of Distributions And Applications, Jasson Vindas Jan 2009

Local Behavior Of Distributions And Applications, Jasson Vindas

LSU Doctoral Dissertations

This dissertation studies local and asymptotic properties of distributions (generalized functions) in connection to several problems in harmonic analysis, approximation theory, classical real and complex function theory, tauberian theory, summability of divergent series and integrals, and number theory. In Chapter 2 we give two new proofs of the Prime Number Theory based on ideas from asymptotic analysis on spaces of distributions. Several inverse problems in Fourier analysis and summability theory are studied in detail. Chapter 3 provides a complete characterization of point values of tempered distributions and functions in terms of a generalized pointwise Fourier inversion formula. The relation of …


Multiple Dataset Visualization (Mdv) Framework For Scalar Volume Data, Gaurav Khanduja Jan 2009

Multiple Dataset Visualization (Mdv) Framework For Scalar Volume Data, Gaurav Khanduja

LSU Doctoral Dissertations

Many applications require comparative analysis of multiple datasets representing different samples, conditions, time instants, or views in order to develop a better understanding of the scientific problem/system under consideration. One effective approach for such analysis is visualization of the data. In this PhD thesis, we propose an innovative multiple dataset visualization (MDV) approach in which two or more datasets of a given type are rendered concurrently in the same visualization. MDV is an important concept for the cases where it is not possible to make an inference based on one dataset, and comparisons between many datasets are required to reveal …


Impulsive Control Systems, Wei Cai Jan 2009

Impulsive Control Systems, Wei Cai

LSU Doctoral Dissertations

Impulsive control systems arose from classical control systems described by differential equations where the control functions could be unbounded. Passing to the limit of trajectories whose velocities are changing very rapidly leads to the state vector to "jump", or exhibit impulsive behavior. The mathematical model in this thesis uses a differential inclusion and a measure-driven control, and it becomes possible to deal with the discontinuity of movements happening over a small interval. We adopt the formulism of impulsive systems in which the velocities are decomposed by the slow and fast ones. The fast time velocity is expressed as the multiplication …


Scanning Probe Microscopy Investigations Of (1) Arrays Of Cysteine-Coated Cds Nanoparticles And (2) Structures Formed During The Early Stages Of The Corrosion Of Copper Surfaces, Brian Robert Lewandowski Jan 2009

Scanning Probe Microscopy Investigations Of (1) Arrays Of Cysteine-Coated Cds Nanoparticles And (2) Structures Formed During The Early Stages Of The Corrosion Of Copper Surfaces, Brian Robert Lewandowski

LSU Doctoral Dissertations

Scanning probe microscopy (SPM) characterizations are becoming more prevalent for surface investigations due to their capabilities for obtaining structural information and physical measurements. New capabilities of SPM for studying and controlling nanoscale processes are emerging as valuable assets in research. A fundamental understanding of the interactions of surface reactions provides essential information for developing workable applications for nanotechnology. Two applications of SPM are discussed in this dissertation. The first investigation uses atomic force microscopy (AFM) for the characterization of nanostructures produced with a newly developed lithographic technique called “two-particle” lithography. This new technique is based on particle lithography for the …


Merged Electrospray Ionization Mass Spectrometry, Jianan Dong Jan 2009

Merged Electrospray Ionization Mass Spectrometry, Jianan Dong

LSU Doctoral Dissertations

Ambient ionization allows the analysis of materials in their native environment without sample preparation by creating ions outside the mass spectrometer. The goal of this research was to develop new ambient ionization techniques for application to solids, liquids and particles under ambient conditions. Samples to be analyzed were directly merged with an electrospray of droplets, and then ionized and detected by a mass spectrometer. An ion trap mass spectrometer was modified with a nanoelectrospray source and configured for three experiments: merged electrospray ionization of dry particles, merged electrospray ionization of combustion products, and infrared laser desorption/ablation using electrospray for post-ionization. …


Task Specific Ionic Liquids For Enantiomeric Recognition And Nanomaterials For Biomedical Imaging, David Kipkogei Bwambok Jan 2009

Task Specific Ionic Liquids For Enantiomeric Recognition And Nanomaterials For Biomedical Imaging, David Kipkogei Bwambok

LSU Doctoral Dissertations

Ionic liquids (ILs) are organic salts that melt at or below 100°C. Interest in ILs continues to grow due to their unique properties such as lack of measurable vapor pressure, high thermal stability, tunability and recyclability. The first part of this dissertation explores the use of chiral ionic liquids (CILs) for enantiomeric recognition of chiral analytes using fluorescence spectroscopy. Chiral analyses continue to be a subject of considerable interest primarily as a result of legislation introduced by the Food and Drug Administration. This has led to an increased need for suitable chiral selectors and methods to verify the enantiomeric forms …


Stochastic Navier-Stokes Equations With Fractional Brownian Motions, Liqun Fang Jan 2009

Stochastic Navier-Stokes Equations With Fractional Brownian Motions, Liqun Fang

LSU Doctoral Dissertations

The aim of this dissertation is to study stochastic Navier-Stokes equations with a fractional Brownian motion noise. The second chapter will introduce the background results on fractional Brownian motions and some of their properties. The third chapter will focus on the Stokes operator and the semigroup generated by this operator. The Navier-Stokes equations and the evolution equation setup will be described in the next chapter. The main goal is to prove the existence and uniqueness of solutions for the stochastic Navier-Stokes equations with a fractional Brownian motion noise under suitable conditions. The proof is given with full details for two …


Studies Of States And State Transitions In Low Mass X-Ray Binaries, Charles Bradley Jan 2009

Studies Of States And State Transitions In Low Mass X-Ray Binaries, Charles Bradley

LSU Doctoral Dissertations

We investigate the model of a disk/coronal accretion flow into a black hole. We build a numerical code to ascertain whether the inner regions of an accretion disk in X-ray binaries can transform from a cool standard disk to an advection-dominated flow through the known properties of Coulomb interaction in a two-temperature plasma, taking into account viscous heating, standard radiation processes, and thermal conduction. A hot, diffuse corona covering the whole disk is powered by accretion, but it exchanges energy with the underlying cool disk through radiative interactions and conduction. If the accretion rate is low enough, at some intermediate …


Miocene Herpetofaunas From The Central Gulf Coast Usa: Their Paleoecology, Biogeography, And Biostratigraphy, Michael John Williams Jan 2009

Miocene Herpetofaunas From The Central Gulf Coast Usa: Their Paleoecology, Biogeography, And Biostratigraphy, Michael John Williams

LSU Doctoral Dissertations

The late Barstovian Fort Polk herpetofauna represents the most diverse herpetofauna on the Gulf Coast, USA, and includes 15 genera from ten families. The herpetofaunal composition of Fort Polk and Miocene east Texas localities is similar enough to Great Plains localities that they are all considered to be one biogeographical province during the Barstovian. The use of ternary diagrams, ratios of herpetological elements to kg matrix screened, and natricine-colubrine indices, has allowed determining the wetness of the Fort Polk sites. Development of a composite stratigraphic section for North American fossil snakes has allowed recognition of two extinctions of fossil snakes …


Improved Seismic Isolation For The Laser Interferometer Gravitational Wave Observatory With Hydraulic External Pre-Isolator System, Shyang Wen Jan 2009

Improved Seismic Isolation For The Laser Interferometer Gravitational Wave Observatory With Hydraulic External Pre-Isolator System, Shyang Wen

LSU Doctoral Dissertations

LIGO hosts the world’s most sensitive GW detectors capable of detecting strain of h=10-22 at 100-200Hz. To maximize the amount of useful scientific results LIGO generates, it is necessary to operate the instrument uninterruptedly. However, for ground-based detectors, this is not possible without isolating it from the environmental disturbances, which in most cases is predominated by seismic noise. We examined the recent seismic noise records at LLO and LHO, and found the seismic noise at both sites had decreased from Oct. 1, 2003 to Oct. 1, 2006. No long term trend can be derived from the there-year data studied, however …


On-Line Laser Desorption/Ionization Mass Spectrometry, Damien A. Narcisse Jan 2009

On-Line Laser Desorption/Ionization Mass Spectrometry, Damien A. Narcisse

LSU Doctoral Dissertations

Interfaces for on-line laser desorption/ionization mass spectrometry are presented in this dissertation. An on line laser desorption interface allows samples to be introduced directly into the mass spectrometer for high-throughput applications. For this research, a linear time of flight mass spectrometer was constructed with an ionization source designed to accept various laser desorption interfaces. A ball inlet interface was used for continuous analyte deposition at atmospheric pressure and vacuum ionization. A solvent-based cleaning system and a separate capillary for MALDI matrix delivery was utilized for continuous on line sampling with the ball inlet interface. Microfluidic devices were brought into contact …


Quantum Nonlinear Optics: Applications To Quantum Metrology, Imaging, And Information, Ryan Glasser Jan 2009

Quantum Nonlinear Optics: Applications To Quantum Metrology, Imaging, And Information, Ryan Glasser

LSU Doctoral Dissertations

The fields of quantum and nonlinear optics have given rise to a variety of nonclassical states of light that have been proven to surpass certain limitations set by classical physics. Namely, certain squeezed and entangled states have been shown to beat the shot-noise limit when making precision phase measurements in interferometry, as well as write lithographic patterns that are smaller than classically allowed by the Rayleigh diffraction limit. Additionally, single-photon sources and entangled photon pairs have given rise to provably secure quantum key distribution for cryptography. Producing these quantum states of light has proven a difficult task. Nonlinear crystals, when …


Algorithms Related To Subgroups Of The Modular Group, Constantin Cristian Caranica Jan 2009

Algorithms Related To Subgroups Of The Modular Group, Constantin Cristian Caranica

LSU Doctoral Dissertations

Classifying subgroups of the modular group PSL_2{Z} is a fundamental problem with applications to modular forms, in addition to its group-theoretic interest. While a lot of research has been done on the congruence subgroups of PSL_2{Z}, very little is known about noncongruence subgroups. The purpose of this thesis is to find and characterize small-index noncongruence subgroups of the modular group PSL_2{Z}. We use the concept of Farey symbol to describe the subgroups of PSL_2{Z}. The first part contains results concerning the geometry of subgroups of PSL_2{Z}. The second part describes a graph-theoretical approach to finding all subgroups of a given …


The Structure Of 4-Separations In 4-Connected Matroids, Jeremy M. Aikin Jan 2009

The Structure Of 4-Separations In 4-Connected Matroids, Jeremy M. Aikin

LSU Doctoral Dissertations

Oxley, Semple and Whittle described a tree decomposition for a 3-connected matroid M that displays, up to a natural equivalence, all non-trivial 3-separations of M. Crossing 3-separations gave rise to fundamental structures known as flowers. In this dissertation, we define generalized flower structure called a k-flower, with no assumptions on the connectivity of M. We completely classify k-flowers in terms of the local connectivity between pairs of petals. Specializing to the case of 4-connected matroids, we give a new notion of equivalence of 4-separations that we show will be needed to describe a tree decomposition for 4-connected matroids. Finally, we …


Atom-Based Computer Simulation Studies Of Gas-To-Liquid Nucleation In Atmospherically Relevant Systems: Clarifying Discrepancies And Elucidating Mechanisms, Ricky Bendanillo Nellas Jan 2009

Atom-Based Computer Simulation Studies Of Gas-To-Liquid Nucleation In Atmospherically Relevant Systems: Clarifying Discrepancies And Elucidating Mechanisms, Ricky Bendanillo Nellas

LSU Doctoral Dissertations

For over a century, nucleation for all systems was thought simplistically to be a process that advances through the formation of critical clusters with a well-defined composition. Our results show intriguing nucleation mechanisms that challenge the aforementioned notion. We employed the simple TraPPE-UA (transferable potential for phase equilibria – united atom) force field and the AVUS-HR approach (a combination of aggregation-volume-bias Monte Carlo, umbrella sampling, and histogram reweighting), to investigate the homogeneous vapor-to-liquid nucleation of various nucleating systems. We found out that these systems could nucleate through a variety of unique non-ideal mechanisms. Alongside existing experimental investigations, this dissertation presents …


Unavoidable Minors In Graphs And Matroids, Carolyn Barlow Chun Jan 2009

Unavoidable Minors In Graphs And Matroids, Carolyn Barlow Chun

LSU Doctoral Dissertations

It is well known that every sufficiently large connected graph G has either a vertex of high degree or a long path. If we require G to be more highly connected, then we ensure the presence of more highly structured minors. In particular, for all positive integers k, every 2-connected graph G has a series minor isomorphic to a k-edge cycle or K_{2,k}. In 1993, Oxley, Oporowski, and Thomas extended this result to 3- and internally 4-connected graphs identifying all unavoidable series minors of these classes. Loosely speaking, a series minor allows for arbitrary edge deletions but only allows edges …