PIMS Special Speakers: Hamilton paths in vertex-transitive graphs

A graph is Hamilton-connected if for any two vertices u and v there is a Hamilton path whose terminal vertices are u and v. Similarly, a bipartite graph is Hamilton-laceable if for any two vertices u and v from distinct parts there is a Hamilton path with terminal vertices u and v. We present a survey of what is known about Hamilton-connected and Hamilton-laceable vertex-transitive graphs.