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.

This course is part of the Introduction to Discrete Mathematics for Computer Science Specialization

# Introduction to Graph Theory

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## About this Course

### Learner Career Outcomes

## 33%

## 50%

## 33%

### Learner Career Outcomes

## 33%

## 50%

## 33%

#### Shareable Certificate

#### 100% online

#### Course 3 of 5 in the

#### Flexible deadlines

#### Beginner Level

#### Approx. 15 hours to complete

#### English

## Syllabus - What you will learn from this course

**3 hours to complete**

## What is a Graph?

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.

**3 hours to complete**

**14 videos**

**5 readings**

**2 practice exercises**

**5 hours to complete**

## CYCLES

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!

**5 hours to complete**

**12 videos**

**4 readings**

**4 practice exercises**

**4 hours to complete**

## Graph Classes

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!

**4 hours to complete**

**11 videos**

**4 readings**

**3 practice exercises**

**4 hours to complete**

## 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. 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.

**4 hours to complete**

**14 videos**

**5 readings**

**4 practice exercises**

### Top reviews from Introduction to Graph Theory

Appreciate the structure and the explanations with examples. The practice tool before every lesson not makes it fun to learn but also sets the student in the context and can anticipate the concept.

Was pretty fun and gave a good intro to graph theory. Definitely felt inspired to go deeper and understood the most basic proof ideas. The later lectures can spike in difficulty though. Very nice!

### About University of California San Diego

### About National Research University Higher School of Economics

## About the Introduction to Discrete Mathematics for Computer Science Specialization

## Frequently Asked Questions

When will I have access to the lectures and assignments?

Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

What will I get if I subscribe to this Specialization?

When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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Is financial aid available?

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