Dr. Zixia Song
Department of Mathematics
University of Central Florida
Abstract: Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-coloring of the edges of a complete graph on N vertices contains a monochromatic copy of H. The existence of these numbers has been known since 1930 but computing Ramsey numbers is a notoriously difficult problem in combinatorics. We study Ramsey numbers of graphs under Gallai colorings, where a Gallai coloring is a coloring of the edges of a complete graph such that no triangle has all its edges colored differently. Gallai-Ramsey numbers are more well-behaved, though computing them is far from trivial. In this talk, I will present our recent results on Gallai-Ramsey numbers of graphs.
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