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Graduate Seminar
Joseph Briggs Carnegie Mellon University Title: Topologists outperforming finite graph theorists in Hamilton decompositions Abstract: One of the oldest results in graph theory says that complete graphs on an $2k+1$ number of vertices can be $k$edge colored with a Hamilton cycle in each color. Because we enjoy coloring finite graphs for a living, many graph theorists have asked which other classes of $2k$regular graphs can be similarly colored. But looks can be deceptive, and 2 straightforwardsounding conjectures in this vain have resisted much progress for 40 years! Remarkably, it has been shown recently that 2 particular countably infinite analogues of these questions have affirmative answers.We will define Cartesian graph products, Cayley graphs, and the notion of an infinite Hamilton cycle that makes most sense from a topological viewpoint here. We will also draw many pictures. Remarkably, it appears that introducing any finiteness makes these problems more difficult! Date: Tuesday, October 24, 2017 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Yangxi Ou Note: Video on Youtube: https://youtu.be/pDhlkMfupI. 