[PAST EVENT] Mathematics Colloquium: Zixia Song (University of Central Florida)
Title: Gallai-Ramsey Numbers of Cycles.
Abstract: Ramsey theory dates back to the 1930s and 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. Given a graph H and apositive integer k, the Gallai-Ramsey number of H is the least positive integer N such that every Gallai coloring of the complete graph K_N using k colors contains a monochromatic copy of H. Gallai-Ramsey numbers of graphs 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 cycles.