Kevin Milans

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Degree Ramsey Numbers of Graphs
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**Abstract:**
In Ramsey Theory, we study when every partition of a large structure yields a
part with additional structure. Theodore Motzkin summarized the field with his
famous quip "Complete disorder is impossible." For graphs, Ramsey's Theorem
implies that for each *G*, every 2-edge-coloring of a sufficiently large
complete graph contains a monochromatic copy of *G*. What properties of
*G* permit us to replace the complete graph with a much sparser host
graph? We explore some partial answers to this question. This is joint work
with Tao Jiang, Bill Kinnersley, and Douglas B. West.