Graph Theory

Graph Theory
Graph Theory by Dr. L. Sunil Chandran, Department of Computer Science and Automation, IISc Bangalore. For more details on NPTEL visit
Mod-01 Lec-01 Introduction: Vertex cover and independent set
Mod-01 Lec-02 Matchings: Konig's theorem and Hall's theorem
Mod-01 Lec-03 More on Hall's theorem and some applications
Mod-01 Lec-04 Tutte's theorem on existence of a perfect matching
Mod-01 Lec-05 More on Tutte's theorem
Mod-01 Lec-06 More on Matchings
Mod-01 Lec-07 Dominating set, path cover
Mod-01 Lec-08 Gallai -- Millgram theorem, Dilworth's theorem
Mod-02 Lec-09 Connectivity: 2-connected and 3- connected graphs
Mod-02 Lec-10 Menger's theorem
Mod-02 Lec-11 More on connectivity: k- linkedness
Mod-02 Lec-12 Minors, topological minors and more on k- linkedness
Mod-03 Lec-13 Vertex coloring: Brooks theorem
Mod-03 Lec-14 More on vertex coloring
Mod-03 Lec-15 Edge coloring: Vizing's theorem
Mod-03 Lec-16 Proof of Vizing's theorem, Introduction to planarity
Mod-03 Lec-17 5- coloring planar graphs, Kuratowsky's theorem
Mod-03 Lec-18 Proof of Kuratowsky's theorem, List coloring
Mod-03 Lec-19 List chromatic index
Mod-03 Lec-20 Adjacency polynomial of a graph and combinatorial Nullstellensatz
Mod-03 Lec-21 Chromatic polynomial, k - critical graphs
Mod-03 Lec-22 Gallai-Roy theorem, Acyclic coloring, Hadwiger's conjecture
Mod-04 Lec-23 Perfect graphs: Examples
Mod-04 Lec-24 Interval graphs, chordal graphs
Mod-04 Lec-25 Proof of weak perfect graph theorem (WPGT)
Mod-04 Lec-26 Second proof of WPGT, Some non-perfect graph classes
Mod-04 Lec-27 More special classes of graphs
Mod-04 Lec-28 Boxicity,Sphericity, Hamiltonian circuits
Mod-04 Lec-29 More on Hamiltonicity: Chvatal's theorem
Mod-04 Lec-30 Chvatal's theorem, toughness, Hamiltonicity and 4-color conjecture
Mod-05 Lec-31 Network flows: Max flow mincut theorem
Mod-05 Lec-32 More on network flows: Circulations
Mod-05 Lec-33 Circulations and tensions
Mod-05 Lec-34 More on circulations and tensions, flow number and Tutte's flow conjectures
Mod-06 Lec-35 Random graphs and probabilistic method: Preliminaries
Mod-06 Lec-36 Probabilistic method: Markov's inequality, Ramsey number
Mod-06 Lec-37 Probabilistic method: Graphs of high girth and high chromatic number
Mod-06 Lec-38 Probabilistic method: Second moment method, Lovasz local lemma
Mod-07 Lec-39 Graph minors and Hadwiger's conjecture