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Full-Text Articles in Physical Sciences and Mathematics
Star Decompositions Of The Complete Split Graph, Adam C. Volk
Star Decompositions Of The Complete Split Graph, Adam C. Volk
Honors Theses
A graph is a discrete mathematical structure that consists of a set of vertices and a set of edges between pairs of vertices. A problem of interest in graph theory is that of graph decomposition, partitioning the set of edges into disjoint sets, producing subgraphs which are isomorphic to each other. Here we consider the problem of decomposing a class of graphs called complete split graphs into stars of a fixed size. We present conditions for the decomposition as well as an algorithm for the decomposition when it is possible.
Results On Some Generalizations Of Interval Graphs, Jonathan David Ashbrock
Results On Some Generalizations Of Interval Graphs, Jonathan David Ashbrock
Honors Theses
An interval graph is the intersection graph of a family of intervals on the real line. Interval graphs are a well-studied class of graphs. Path graphs are a generalization of interval graphs and are defined to be the intersection graphs of a family of paths in a tree. In this thesis, we study path graphs which are representable in a subdivided K1, 3. Our main results are a characterization theorem and a polynomial time algorithm for recognition of this class of graphs. The second section of this thesis provides a bound for a graph parameter, the boxicity of …
Domain Representability And Topological Completeness, Matthew D. Devilbiss
Domain Representability And Topological Completeness, Matthew D. Devilbiss
Honors Theses
Topological completeness properties seek to generalize the definition of complete metric space to the context of topologies. Chapter 1 gives an overview of some of these properties. Chapter 2 introduces domain theory, a field originally intended for use in theoretical computer science. Finally, Chapter 3 examines how this computer-scientific notion can be employed in the study of topological completeness in the form of domain representability. The connections between domain representability and other topological completeness properties are subsequently examined.
Global And Regional Chitinozoan Biodiversity Dynamics In The Ordovician: Relationships To Sea-Level, Carbon Cycling And Tectonics, Jordan Watson
Global And Regional Chitinozoan Biodiversity Dynamics In The Ordovician: Relationships To Sea-Level, Carbon Cycling And Tectonics, Jordan Watson
Honors Theses
Fossil species provide extensive information about the past history of life on Earth. This thesis focuses on the global and regional biodiversity dynamics of the extinct fossil group Chitinozoa, and analyzes the impact and influences of sea-level, global carbon cycling and tectonics on their biodiversity. Biodiversity curves were generated from three different paleo-continents, Laurentia, Baltica, and Gondwana using the automated graphic correlation computer program CONOP9. Traditional methods of biodiversity analysis count fossil taxa in individual intervals of geologic time. The results of these methods are highly dependent upon interval length and the relationship of taxon range to interval boundaries. CONOP9 …