UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

More information is available at Theses and Dissertations at University of Maryland Libraries.

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Author: search.filters.author.Brady, RobertSubject: search.filters.subject.pedagogy

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    A Pedagogical Approach to Ramsey Multiplicity
    (2023) Brady, Robert; Gasarch, William; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    It 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.