Mod-06 Lec-35 Random graphs and probabilistic method: Preliminaries

Course Lectures

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

  Dr. L. Sunil Chandran

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

  Dr. L. Sunil Chandran

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

  Dr. L. Sunil Chandran

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• Mod-01 Lec-04 Tutte's theorem on existence of a perfect matching

  Dr. L. Sunil Chandran

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• Mod-01 Lec-05 More on Tutte's theorem

  Dr. L. Sunil Chandran

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• Mod-01 Lec-06 More on Matchings

  Dr. L. Sunil Chandran

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• Mod-01 Lec-07 Dominating set, path cover

  Dr. L. Sunil Chandran

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• Mod-01 Lec-08 Gallai -- Millgram theorem, Dilworth's theorem

  Dr. L. Sunil Chandran

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• Mod-02 Lec-09 Connectivity: 2-connected and 3- connected graphs

  Dr. L. Sunil Chandran

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• Mod-02 Lec-10 Menger's theorem

  Dr. L. Sunil Chandran

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• Mod-02 Lec-11 More on connectivity: k- linkedness

  Dr. L. Sunil Chandran

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• Mod-02 Lec-12 Minors, topological minors and more on k- linkedness

  Dr. L. Sunil Chandran

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• Mod-03 Lec-13 Vertex coloring: Brooks theorem

  Dr. L. Sunil Chandran

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• Mod-03 Lec-14 More on vertex coloring

  Dr. L. Sunil Chandran

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• Mod-03 Lec-15 Edge coloring: Vizing's theorem

  Dr. L. Sunil Chandran

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• Mod-03 Lec-16 Proof of Vizing's theorem, Introduction to planarity

  Dr. L. Sunil Chandran

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• Mod-03 Lec-17 5- coloring planar graphs, Kuratowsky's theorem

  Dr. L. Sunil Chandran

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• Mod-03 Lec-18 Proof of Kuratowsky's theorem, List coloring

  Dr. L. Sunil Chandran

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• Mod-03 Lec-19 List chromatic index

  Dr. L. Sunil Chandran

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• Mod-03 Lec-20 Adjacency polynomial of a graph and combinatorial Nullstellensatz

  Dr. L. Sunil Chandran

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• Mod-03 Lec-21 Chromatic polynomial, k - critical graphs

  Dr. L. Sunil Chandran

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• Mod-03 Lec-22 Gallai-Roy theorem, Acyclic coloring, Hadwiger's conjecture

  Dr. L. Sunil Chandran

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• Mod-04 Lec-23 Perfect graphs: Examples

  Dr. L. Sunil Chandran

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• Mod-04 Lec-24 Interval graphs, chordal graphs

  Dr. L. Sunil Chandran

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• Mod-04 Lec-25 Proof of weak perfect graph theorem (WPGT)

  Dr. L. Sunil Chandran

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• Mod-04 Lec-26 Second proof of WPGT, Some non-perfect graph classes

  Dr. L. Sunil Chandran

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• Mod-04 Lec-27 More special classes of graphs

  Dr. L. Sunil Chandran

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• Mod-04 Lec-28 Boxicity,Sphericity, Hamiltonian circuits

  Dr. L. Sunil Chandran

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• Mod-04 Lec-29 More on Hamiltonicity: Chvatal's theorem

  Dr. L. Sunil Chandran

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• Mod-04 Lec-30 Chvatal's theorem, toughness, Hamiltonicity and 4-color conjecture

  Dr. L. Sunil Chandran

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• Mod-05 Lec-31 Network flows: Max flow mincut theorem

  Dr. L. Sunil Chandran

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• Mod-05 Lec-32 More on network flows: Circulations

  Dr. L. Sunil Chandran

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• Mod-05 Lec-33 Circulations and tensions

  Dr. L. Sunil Chandran

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• Mod-05 Lec-34 More on circulations and tensions, flow number and Tutte's flow conjectures

  Dr. L. Sunil Chandran

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• Mod-06 Lec-35 Random graphs and probabilistic method: Preliminaries

  Dr. L. Sunil Chandran

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• Mod-06 Lec-36 Probabilistic method: Markov's inequality, Ramsey number

  Dr. L. Sunil Chandran

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• Mod-06 Lec-37 Probabilistic method: Graphs of high girth and high chromatic number

  Dr. L. Sunil Chandran

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• Mod-06 Lec-38 Probabilistic method: Second moment method, Lovasz local lemma

  Dr. L. Sunil Chandran

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• Mod-07 Lec-39 Graph minors and Hadwiger's conjecture

  Dr. L. Sunil Chandran

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• Mod-07 Lec-40 More on graph minors, tree decompositions

  Dr. L. Sunil Chandran

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