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Full-Text Articles in Physical Sciences and Mathematics
Results On Edge-Colored Graphs And Pancyclicity, James Carraher
Results On Edge-Colored Graphs And Pancyclicity, James Carraher
Department of Mathematics: Dissertations, Theses, and Student Research
This thesis focuses on determining when a graph with additional structure contains certain subgraphs, particularly circuits, cycles, or trees. The specific problems and presented results include a blend of many fundamental graph theory concepts such as edge-coloring, routing problems, decomposition problems, and containing cycles of various lengths. The three primary chapters in this thesis address the problems of finding eulerian circuits with additional restrictions, decomposing the edge-colored complete graph K_n into rainbow spanning trees, and showing a 4-connected claw-free and N(3,2,1)-free graph is pancyclic.
Adviser: Stephen G. Hartke
Combinatorial And Algebraic Coding Techniques For Flash Memory Storage, Kathryn A. Haymaker
Combinatorial And Algebraic Coding Techniques For Flash Memory Storage, Kathryn A. Haymaker
Department of Mathematics: Dissertations, Theses, and Student Research
Error-correcting codes are used to achieve reliable and efficient transmission when storing or sending information across a noisy channel. This thesis investigates a mathematical approach to coding techniques for storage devices such as flash memory storage, although many of the resulting codes and coding schemes can be applied in other contexts. The main contributions of this work include the design of efficient codes and decoding algorithms using discrete structures such as graphs and finite geometries, and developing a variety of strategies for adapting codes to a multi-level setting.
Information storage devices are prone to errors over time, and the frequency …