Graph Theory

Graph Theory. Instructor: Dr. L. Sunil Chandran, Department of Computer Science and Automation, IISc Bangalore. In computer science, graph theory is used extensively. The aim of this course is to introduce the subject of graph theory to computer science students in a thorough way. While the course will cover all elementary concepts such as coloring, covering, hamiltonicity, planarity, connectivity and so on, it will also introduce the students to some advanced concepts. (from


Covering Problems
Lecture 01 - Introduction: Vertex Cover and Independent Set
Lecture 02 - Matchings: Konig's Theorem and Hall's Theorem
Lecture 03 - More on Hall's Theorem and Some Applications
Lecture 04 - Tutte's Theorem on Existence of a Perfect Matching
Lecture 05 - More on Tutte's Theorem
Lecture 06 - More on Matchings
Lecture 07 - Dominating Set, Path Cover
Lecture 08 - Gallai-Milgram Theorem, Dilworth's Theorem
Lecture 09 - Connectivity: 2-Connected and 3-Connected Graphs
Lecture 10 - Menger's Theorem
Lecture 11 - More on Connectivity: K-Linkedness
Lecture 12 - Minors, Topological Minors and More on K-Linkedness
Lecture 13 - Vertex Coloring: Brooks' Theorem
Lecture 14 - More on Vertex Coloring
Lecture 15 - Edge Coloring: Vizing's Theorem
Lecture 16 - Proof of Vizing's Theorem, Introduction to Planarity
Lecture 17 - 5-Coloring Planar Graphs, Kuratowski's Theorem
Lecture 18 - Proof of Kuratowski's Theorem, List Coloring
Lecture 19 - List Chromatic Index
Lecture 20 - Adjacency Polynomial of a Graph and Combinatorial Nullstellensatz
Lecture 21 - Chromatic Polynomial, K-Critical Graphs
Lecture 22 - Gallai-Roy Theorem, Acyclic Coloring, Hadwiger Conjecture
Special Classes of Graphs
Lecture 23 - Perfect Graphs: Examples
Lecture 24 - Interval Graphs, Chordal Graphs
Lecture 25 - Proof of Weak Perfect Graph Theorem (WPGT)
Lecture 26 - Second Proof of WPGT, Some Non-perfect Graph Classes
Lecture 27 - More Special Classes of Graphs
Lecture 28 - Boxicity, Sphericity, Hamiltonian Circuits
Lecture 29 - More on Hamiltonicity: Chvatal's Theorem
Lecture 30 - Chvatal's Theorem, Toughness, Hamiltonicity and 4-Color Conjecture
Network Flows
Lecture 31 - Network Flows: Max-Flow Min-Cut Theorem
Lecture 32 - More on Network Flows: Circulations
Lecture 33 - Circulations and Tensions
Lecture 34 - More on Circulations and Tensions, Flow Number and Tutte's Flow Conjectures
Random Graphs and Probabilistic Method
Lecture 35 - Random Graphs and Probabilistic Method: Preliminaries
Lecture 36 - Probabilistic Method: Markov's Inequality, Ramsey Number
Lecture 37 - Probabilistic Method: Graphs of High Girth and High Chromatic Number
Lecture 38 - Probabilistic Method: Second Moment Method, Lovasz Local Lemma
Graph Minors
Lecture 39 - Graph Minors and Hadwiger Conjecture
Lecture 40 - More on Graph Minors, Tree Decompositions

Graph Theory
Instructor: Dr. L. Sunil Chandran, Department of Computer Science and Automation, IISc Bangalore. An introduction to the subject of graph theory.