{"id":{"repo_id":"calpoly","oai_identifier":"oai:digitalcommons.calpoly.edu:theses-4050"},"canonical_url":"https://search.dev.ndltd.org/etd/calpoly/oai:digitalcommons.calpoly.edu:theses-4050","repository":{"repo_id":"calpoly","name":"Cal Poly","base_url":"https://digitalcommons.calpoly.edu/do/oai/"},"display":{"title":"Ramsey Theory","abstract":"<p>The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the complete graph $K_{R(r, b)}$ with colors red and blue either embeds a red $K_r$ or a blue $K_b$. We explore various methods to find lower bounds on $R(r,b)$, finding new results on fibrations and semicirculant graphs. Then, generalizing the Ramsey number to graphs other than complete graphs, we flesh out the missing details in the literature on a theorem that completely determines the generalized Ramsey number for cycles.</p>","abstract_html":"&lt;p&gt;The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the complete graph <span class=\"etd-inline-math\">K<sub>R(r, b)</sub></span> with colors red and blue either embeds a red <span class=\"etd-inline-math\">K<sub>r</sub></span> or a blue <span class=\"etd-inline-math\">K<sub>b</sub></span>. We explore various methods to find lower bounds on $R(r,b)$, finding new results on fibrations and semicirculant graphs. Then, generalizing the Ramsey number to graphs other than complete graphs, we flesh out the missing details in the literature on a theorem that completely determines the generalized Ramsey number for cycles.&lt;/p&gt;","abstract_has_math":true,"creators":["Lai, David"],"institution":null,"degree_name":"MS in Mathematics","degree_level":null,"degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Anthony Mendes","Mathematics","College of Science and Mathematics"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-06-01T07:00:00Z","date_published":"2022-06-01T07:00:00Z","updated_at":"2026-07-24T01:32:13Z","subjects":["Mathematics","Graph Theory","Ramsey Theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.15368/theses.2022.41"],"render_values":[{"text":"10.15368/theses.2022.41","href":"https://doi.org/10.15368/theses.2022.41","code":true}]}]},"links":{"outbound_url":"https://digitalcommons.calpoly.edu/theses/2621","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Anthony Mendes","Mathematics","College of Science and Mathematics"]},{"key":"dc:creator","label":"Author","values":["Lai, David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2022-06-07T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Graph Theory","Ramsey Theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.calpoly.edu/theses/2621","10.15368/theses.2022.41"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the complete graph $K_{R(r, b)}$ with colors red and blue either embeds a red $K_r$ or a blue $K_b$. We explore various methods to find lower bounds on $R(r,b)$, finding new results on fibrations and semicirculant graphs. Then, generalizing the Ramsey number to graphs other than complete graphs, we flesh out the missing details in the literature on a theorem that completely determines the generalized Ramsey number for cycles.</p>"]},{"key":"dc:title","label":"Title","values":["Ramsey Theory"]}]}],"canonical_facts":{"dc:contributor":["Anthony Mendes","Mathematics","College of Science and Mathematics"],"dc:creator":["Lai, David"],"dc:date.available":["2022-06-07T07:00:00Z"],"dc:description.abstract":["<p>The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the complete graph $K_{R(r, b)}$ with colors red and blue either embeds a red $K_r$ or a blue $K_b$. We explore various methods to find lower bounds on $R(r,b)$, finding new results on fibrations and semicirculant graphs. Then, generalizing the Ramsey number to graphs other than complete graphs, we flesh out the missing details in the literature on a theorem that completely determines the generalized Ramsey number for cycles.</p>"],"dc:identifier":["https://digitalcommons.calpoly.edu/theses/2621","10.15368/theses.2022.41"],"dc:subject":["Mathematics","Graph Theory","Ramsey Theory"],"dc:title":["Ramsey Theory"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_name":["MS in Mathematics"]},"updated_at":"2026-07-24T01:32:13Z"}