Mod-01 Lec-01 Introduction-Vertex cover and independent set

Duration 0h 57m

Mod-01 Lec-02 Matchings-Konig's theorem and Hall's theorem

Duration 0h 59m

Mod-01 Lec-03 More on Hall's theorem and some applications

Duration 0h 58m

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

Duration 0h 56m

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

Duration 0h 55m

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