Advanced Graph Theory Credits: 4 Discipline: MTH UG/ PG/ UG+PG: UG+PG Pre-requisites Graph Theory – MTH303 or a course with similar content in another institute Anti-requisites None Post Condition (on student capability after successfully completing the course):
The student has deep understanding of graph theory and various advanced results. The student can write proofs for advanced properties/results of graphs. The student is able to do an independent study on a research problem in graph theory and/or use graph theory to model and solve real-life problems.
Brief Description This is an advanced course in graph theory. The topics include Theory of Hypergraphs, Ramsey Theory, Topological Graph Theory, Structural Graph Theory, Extremal Graph Theory, Combinatorial Design and Random Graphs. The primary objective of this course is to introduce students to the research areas in advanced graph theory. Students interested to apply graph theoretic techniques towards modeling and designing algorithms for real-life problems will benefit from the theory of hypergraphs and random graphs. Week 1 2 3 4 5 6 7 8 9 10 11 12 13
Topics Covered Revision of Graph Theory Hypergraphs: General Concepts Hypergraph Coloring Matchings in Hypergraphs Ramsey's Theorem for Graphs Ramsey's Theorem for Hypergraphs Embedding Graphs on Surfaces Introduction to Graph Minor Theory Turan's Theorem and Mantel's Theorem Introduction to Regularity Lemma Balanced Incomplete Block Design Erdos-Renyi Random Graph Barabasi-Albert Random Graph
Evaluation: Equal weightage on each presentation of one hour duration every week.
Texts 1. R. Deistel. Graph Theory. 2. C. Berge. Hypergraphs. Reference Books 1. J. Bondy and U. Murthy. Graph Theory with Applications. 2. B. Bollobas. Extremal Graph Theory. 3. Alan Frieze and Mihal Karonski. Introduction to Random Graphs. 4. B. Bollobas. Random Graphs. 5. Svante Janson, Thomas Luczak, Andrzej Rucinski. Random Graphs. 6. J. Kleinberg. Networks, Crowds and Markets. 7. M. Newman. Networks: An Introduction.
The student is able to do an independent study on a research problem in graph ... Ramsey Theory, Topological Graph Theory, Structural Graph Theory, Extremal ...
Less compute intensive due to elimination stages. â Not dependent on singularities, so robust against partial prints. â Should be robust against distortions.
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Conclusions & Future work. â Not dependent on singularities, so robust against partial prints. â Should be robust against distortions. â Time and Space efficient. â Results to be checked on a larger database. â Water reservoir approach to b
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