We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. Graph Theory gives us, both an easy way to pictorially represent many major mathematical results, and insights into the deep theories behind them.
Introduction to Graph Theory
This course is part of Introduction to Discrete Mathematics for Computer Science Specialization
Instructors: Alexander S. Kulikov
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There are 5 modules in this course
What are graphs? What do we need them for? This week we'll see that a graph is a simple pictorial way to represent almost any relations between objects. We'll see that we use graph applications daily! We'll learn what graphs are, when and how to use them, how to draw graphs, and we'll also see the most important graph classes. We start off with two interactive puzzles. While they may be hard, they demonstrate the power of graph theory very well! If you don't find these puzzles easy, please see the videos and reading materials after them.
What's included
14 videos6 readings5 assignments1 ungraded lab
We’ll consider connected components of a graph and how they can be used to implement a simple program for solving the Guarini puzzle and for proving optimality of a certain protocol. We’ll see how to find a valid ordering of a to-do list or project dependency graph. Finally, we’ll figure out the dramatic difference between seemingly similar Eulerian cycles and Hamiltonian cycles, and we’ll see how they are used in genome assembly!
What's included
12 videos4 readings7 assignments5 ungraded labs
This week we will study three main graph classes: trees, bipartite graphs, and planar graphs. We'll define minimum spanning trees, and then develop an algorithm which finds the cheapest way to connect arbitrary cities. We'll study matchings in bipartite graphs, and see when a set of jobs can be filled by applicants. We'll also learn what planar graphs are, and see when subway stations can be connected without intersections. Stay tuned for more interactive puzzles!
What's included
11 videos4 readings6 assignments2 ungraded labs
We'll focus on the graph parameters and related problems. First, we'll define graph colorings, and see why political maps can be colored in just four colors. Then we will see how cliques and independent sets are related in graphs. Using these notions, we'll prove Ramsey Theorem which states that in a large system, complete disorder is impossible! Finally, we'll study vertex covers, and learn how to find the minimum number of computers which control all network connections.
What's included
14 videos5 readings8 assignments1 ungraded lab
This week we'll develop an algorithm that finds the maximum amount of water which can be routed in a given water supply network. This algorithm is also used in practice for optimization of road traffic and airline scheduling. We'll see how flows in networks are related to matchings in bipartite graphs. We'll then develop an algorithm which finds stable matchings in bipartite graphs. This algorithm solves the problem of matching students with schools, doctors with hospitals, and organ donors with patients. By the end of this week, we'll implement an algorithm which won the Nobel Prize in Economics!
What's included
13 videos6 readings4 assignments
Instructors
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Recommended if you're interested in Algorithms
Rice University
University of Colorado Boulder
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Shanghai Jiao Tong University
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Reviewed on Nov 24, 2017
This course is really good. If someone has interest in graph theory or he wants to learn it, then this course is definitely a good start.
Reviewed on Oct 11, 2020
Great, informative courses. I liked that they are NOT focusing much on Python. I am more confident now with Graphs and its application
Reviewed on Dec 11, 2017
A good course with proper explanation. The mathematical proof of this course is generally easy to understand although a small part of them are vague
New to Algorithms? Start here.
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