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Graph Theory
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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

    57m <?php echo $alt; ?>
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    Proof of Kuratowskys theorem, List coloring

    56m <?php echo $alt; ?>
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    List chromatic index

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    Adjacency polynomial of a graph and combinatorial Nullstellensatz

    56m <?php echo $alt; ?>
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    Chromatic polynomial, k - critical graphs

    57m <?php echo $alt; ?>
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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

    59m <?php echo $alt; ?>
Graph Theory

Network Flows

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

    57m <?php echo $alt; ?>
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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

    56m <?php echo $alt; ?>
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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