Random K-Out Subgraph Leaves Only O-N-K- Inter-Component Edges

This course aims to teach students how to construct a random k-out subgraph that leaves only O(n/k) inter-component edges. The learning outcomes include understanding the concept of random k-out subgraphs, learning how to sample and remove edges effectively, and exploring the challenges involved in constructing such subgraphs. The course covers topics such as general graphs, dense graphs, connectivity, and applications of random subgraphs. The teaching method involves presenting examples, discussing previous studies, providing a high-level proof, and demonstrating the process of sampling and removing edges. This course is intended for individuals interested in graph theory, network analysis, and algorithm design.