Kevin Milans

Degree Ramsey Numbers of Graphs

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.