Advanced Graph Theory

Advanced Graph Theory. Instructor: Prof. Rajiv Misra, Department of Computer Science and Engineering, IIT Patna. Advanced Graph Theory focuses on problem solving using the most important notions of graph theory with an in-depth study of concepts on the applications in the field of computer science. This course provides an in-depth understanding of Graphs and fundamental principles and models underlying the theory, algorithms, and proof techniques in the field of Graph Theory. Emerging applications of Graph Theory in Computer Science domain will be covered for significant impact. Upon completing this course, students will have intimate knowledge about how the graph theory play an important role to solve the technology driven and research oriented problems. (from

Lecture 15 - Network Flow Problems

In this lecture, we will discuss the Network Flow Problems i.e. Maximum Network Flow, f-augmenting path, Ford-Fulkerson labeling algorithm, Max-flow Min-cut Theorem and the Proof of Menger's Theorem using max-flow min-cut theorem.

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Lecture 01 - Graph Theory: Introduction
Lecture 02 - Paths, Cycles, and Trails
Lecture 03 - Eulerian Circuits, Vertex Degrees and Counting
Lecture 04 - The Chinese Postman Problem and Graphic Sequences
Lecture 05 - Trees and Distance
Lecture 06 - Spanning Trees and Enumeration
Lecture 07 - Matchings and Covers
Lecture 08 - Independent Sets, Covers and Maximum Bipartite Matching
Lecture 09 - Weighted Bipartite Matching
Lecture 10 - Stable Matchings and Faster Bipartite Matching
Lecture 11 - Factors and Perfect Matching in General Graphs
Lecture 12 - Matching in General Graphs: Edmonds' Blossom Algorithm
Lecture 13 - Connectivity and Paths: Cuts and Connectivity
Lecture 14 - k-Connected Graphs
Lecture 15 - Network Flow Problems
Lecture 16 - Vertex Coloring and Upper Bounds
Lecture 17 - Brooks' Theorem and Color Critical Graphs
Lecture 18 - Counting Proper Colorings
Lecture 19 - Planar Graphs
Lecture 20 - Characterization of Planar Graphs
Lecture 21 - Line Graphs and Edge-Coloring
Lecture 22 - Hamiltonian Graphs, Traveling Salesman Problem and NP-Completeness
Lecture 23 - Connected Dominating Set and Distributed Algorithm