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Graduate Seminar
Lisa Espig Carnegie Mellon University Title: Threshold for Zebraic Hamilton Cycles in Random Graphs Abstract: When studying random graphs, we often want to know the threshold for the emergence of a particular structure. In other words, in the Erd\"osR\'enyi random graph model $G_{n,p}$  where we consider a graph on $n$ vertices with each edge appearing randomly with probability $p$, how large must $p$ be in order to guarantee certain structures appear in the graph with high probability? Say a perfect matching, or a Hamilton cycle? This and other thresholds are wellstudied. I'll talk a bit about this and the general 'anatomy of random graphs.' Then we will find the threshold for a different kind of structure, involving random graphs with edge colorings. Namely, we will find the threshold for which a randomly 2colored random graph contains a zebraic Hamilton cycle  one whose edges alternate between the two colors, black and white (hence the silly name). Date: Thursday, March 28, 2013 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Brian Kell 