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Graph Theory
broucher Course Brochure
Graph Theory
by Dr. L. Sunil Chandran

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges l...

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About This Course

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges l...

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Course Curriculum
7 Sections | 39 Lecture | 37h 19min total length
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Graph Theory

Covering Problems

| 07h 43min total length
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    Introduction: Vertex cover and independent set

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    Matchings: Konigs theorem and Halls theorem

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    More on Halls theorem and some applications

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    Tuttes theorem on existence of a perfect matching

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    More on Tuttes theorem

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    More on Matchings

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    Dominating set, path cover

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    Gallai : Millgram theorem, Dilworths theorem

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Graph Theory

Connectivity

| 02h 49min total length
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    Connectivity: 2-connected and 3- connected graphs

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    Mengers theorem

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    More on connectivity: k- linkedness

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Graph Theory

Coloring

| 09h 26min total length
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    Vertex coloring: Brooks theorem

    57m <?php echo $alt; ?>
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    More on vertex coloring

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    Edge coloring: Vizing's theorem

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    Proof of Vizings theorem, Introduction to planarity

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    5- coloring planar graphs, Kuratowskys theorem

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    Proof of Kuratowskys theorem, List coloring

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    List chromatic index

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    Adjacency polynomial of a graph and combinatorial Nullstellensatz

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    Chromatic polynomial, k - critical graphs

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    Gallai-Roy theorem, Acyclic coloring, Hadwigers conjecture

    54m <?php echo $alt; ?>
Graph Theory

Special Classes of Graphes

| 07h 40min total length
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    Perfect graphs: Examples

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    Interval graphs, chordal graphs

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    Proof of weak perfect graph theorem (WPGT)

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    Second proof of WPGT, Some non-perfect graph classes

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    More special classes of graphs

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    Boxicity,Sphericity, Hamiltonian circuits

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    More on Hamiltonicity: Chvatals theorem

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    Chvatals theorem, toughness, Hamiltonicity and 4-color conjecture

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Graph Theory

Network Flows

| 03h 51min total length
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    Network flows: Max flow mincut theorem

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    More on network flows: Circulations

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    Circulations and tensions

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    More on circulations and tensions, flow number and Tuttes flow conjectures

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Graph Theory

Random graphs and Probabilistics method

| 03h 52min total length
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    Random graphs and probabilistic method: Preliminaries

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    Probabilistic method: Markovs inequality, Ramsey number

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    Probabilistic method: Graphs of high girth and high chromatic number

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    Probabilistic method: Second moment method, Lovasz local lemma

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Graph Theory

Graph Minors

| 01h 56min total length
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    Graph minors and Hadwigers conjecture

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    More on graph minors, tree decompositions

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show 4 more sections
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