A Pedagogical Approach to Ramsey Multiplicity

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dc.contributor.advisorGasarch, Williamen_US
dc.contributor.authorBrady, Roberten_US
dc.contributor.departmentComputer Scienceen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2024-02-10T06:43:19Z
dc.date.available2024-02-10T06:43:19Z
dc.date.issued2023en_US
dc.description.abstractIt is well known that for all 2-colorings of the edges of $K_6$ there is amonochromatic triangle. Less well known is that there are two monochromatic triangles. More generally, for all 2-colorings of the edges of $K_n$ there are roughly $\ge n^3/24$ monochromatic triangles. Another way to state this is that the density of monochromatic triangles is at least $1/4$. The Ramsey Multiplicity of $k$ is (asymptotically) the greatest $\alpha$ such that for every coloring of $K_n$ the density of monochromatic $K_k$'s is $\alpha$. This concept has been studied for many years. We survey the area and provide proofs that are more complete, more motivated, and using modern notation.en_US
dc.identifierhttps://doi.org/10.13016/dspace/5b6r-ejqq
dc.identifier.urihttp://hdl.handle.net/1903/31701
dc.language.isoenen_US
dc.subject.pqcontrolledComputer scienceen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledTheoretical mathematicsen_US
dc.subject.pquncontrolledgraph-coloringen_US
dc.subject.pquncontrolledpedagogyen_US
dc.subject.pquncontrolledtheoryen_US
dc.titleA Pedagogical Approach to Ramsey Multiplicityen_US
dc.typeThesisen_US

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