Lecture

Graph Theory Basics

Related lectures (30)

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Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.

Graph Coloring: Theory and Applications

Covers the theory and applications of graph coloring, focusing on disassortative stochastic block models and planted coloring.

Graph Coloring: Basics and Applications

Covers the basics and applications of graph coloring, including balancing vectors and achieving perfect fairness.

Markov Chains: Applications and Analysis

Explores Markov chains, focusing on the coloring problem and algorithm analysis.

Information Theory: Basics

Covers the basics of information theory, entropy, and fixed points in graph colorings and the Ising model.

Belief Propagation for Graph Coloring

Explores Belief Propagation for graph coloring and its convergence properties.

Graph Algorithms II: Traversal and Paths

Explores graph traversal methods, spanning trees, and shortest paths using BFS and DFS.

Graphical Models: Representing Probabilistic Distributions

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Graph Coloring: Random vs Symmetrical

Compares random and symmetrical graph coloring in terms of cluster colorability and equilibrium.

Graph Coloring and Directed Cycles

Explores graph coloring, directed cycles, LLL algorithm applications, and element dependencies in graphs.

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Cheeger's Inequalities

Explores Cheeger's inequalities for random walks on graphs and their implications.

Unweighted Bipartite Matching

Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.

Graph Theory Fundamentals

Explores fundamental graph theory concepts, Erdős' results, Chromatic Lemma, and Union Bound theorem in graph theory.

Graphical Models: Probability Distributions and Factor Graphs

Covers graphical models for probability distributions and factor graphs representation.

Networked Control Systems: Opportunities

Explores coordination in networked control systems, graph theory, and consensus algorithms.

Markov Chains and Algorithm Applications

Covers the fundamentals of Markov chains and their applications in algorithms, focusing on proper coloring and the Metropolis algorithm.

Subgraphs vs Induced Subgraphs

Distinguishes between subgraphs and induced subgraphs in graph theory, illustrating the construction of minimal spanning trees.

Graph Sketching: Connected Components

Covers the concept of graph sketching with a focus on connected components.