2026-09-21T00:41:28Zhttps://api.mountainscholar.org/server/oai/requestoai:mountainscholar.org:10217/2377372025-12-30T03:43:24Zcom_10217_100532com_10217_100000com_10217_100468com_10217_100303col_10217_100538col_10217_100469
Frederick, Christopher Austin, author
Peterson, Chris, advisor
2024-03-13T19:26:18Z
2024-03-13T19:26:18Z
2008
ETDF_Frederick_2008_3346425.pdf
https://hdl.handle.net/10217/237737
https://doi.org/10.25675/3.019026
Ramsey Theory is the investigation of edge-colored graphs which force a monochromatic subgraph. We devise a way of breaking certain Ramsey Theory problems into "smaller" pieces so that information about Ramsey Theory can be gained without solving the entire problem, (which is often difficult to solve). Next the work with Ramsey Regions for graphs is translated into the language of hypergraphs. Theorems and techniques are reworked to fit appropriately into the setting of hypergraphs. The work of persistence complex on large data sets is examined in the setting of graphs. Various simplicial complexes can be assigned to a graph. For a given simplicial complex the persistence complex can be constructed, giving a highly detailed graph invariant. Connections between the graph and persistence complex are investigated.
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doctoral dissertations
English
eng
Colorado State University. Libraries
2000-2019
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graph theory
homology tables
Ramsey regions
mathematics
Ramsey regions and simplicial homology tables for graphs
Text
Doctor of Philosophy (Ph.D.)
Doctoral
Mathematics
Colorado State University
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