# Guide Introduction to Graph Theory Contents:

Add as "Interested" to get notified of this course's next session. Go to class. Start now for free! Sign up. 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. In this course, among other intriguing applications, we will see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors.

## Introduction to Graph Theory

We will study Ramsey Theory which proves that in a large system, complete disorder is impossible! By the end of the course, we will implement an algorithm which finds an optimal assignment of students to schools. This algorithm, developed by David Gale and Lloyd S. Shapley, was later recognized by the conferral of Nobel Prize in Economics. As prerequisites we assume only basic math e. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.

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## Introduction to Graph Theory

Write to us: coursera hse. What is a Graph? 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. Graph Classes -This week we will study three main graph classes: trees, bipartite graphs, and planar graphs.

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• Introduction to graph theory.

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! Graph Parameters -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.

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• Introduction To Graph Theory Applications.
• GRAPH DEFINITION AND SOME REAL WORLD PROBLEMS.

Introduction to Graph Theory Number of credits 7. About the course The course treats grapph theoretical notions and problems, and the use of algorithms, both in the mathematical theory of graphs and its applications. In the course, the basic theory of graphs of different kinds is developed in detail, especially trees and bipartite graphs.

## Introduction to Graph Theory

In the course some of the algorithms that totally or partly solve graph theoretical problems are presented. An example of such a problem is to find a matching of maximum weight, and another is to find a maximum flow in a network. The theory for matchings and Hall's theorem are treated, as well as spanning trees and Menger's theorem. Further, the theory of vertex and edge colouring, including Brooks' theorem and Vizing's theorem, are presented. Finally, an introduction to matroid theory is included. Application and eligibility Introduction to Graph Theory, 7.

Starts 25 March Required Knowledge The course requires courses in Mathematics, minimum 60 ECTS or at least two years of university studies and in both cases a course in discrete mathematics, minimum 7,5 ECTS or equivalent.