Explore the fascinating world of graph theory and fixed-parameter tractability in this 39-minute ACM conference talk. Delve into counting patterns in exponential time, understand the concept of fixed-parameter tractability, and discover galactic algorithms. Learn about disjoint general graphs, goals, and schemas while examining key algorithms. Investigate the roles of Daniel, minors, and topological minors as three key players in this field. Gain valuable insights into advanced computational concepts and their applications in solving complex graph-related problems.