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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 nptel.ac.in)

Lecture 32 - More on Network Flows: Circulations

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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

Connectivity

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

Coloring

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