# Suggestions for Graduate-Level Combinatorics/Graph Theory Texts

• ehrenfest
In summary, combinatorics is a branch of mathematics that deals with counting, arranging, and selecting objects or elements without repetition. Graph theory, a subfield of combinatorics, studies graphs used to model pairwise relationships between objects. These fields are important due to their numerous applications in various industries, providing tools for problem-solving and decision-making. They are used in real-world problems such as network design, scheduling, coding theory, and cryptography, as well as in social and biological networks. Recommended texts for studying these topics at a graduate level include "Combinatorics and Graph Theory" by Harris, Hirst, and Mossinghoff, "Introduction to Graph Theory" by West, and "Enumerative Combinatorics" by Stanley.
ehrenfest
I have taken an undergraduate course in combinatorics (and graph theory). I am looking for a graduate-level text at that does everything completely rigorouslym and is suitable for self-study. Any suggestions?

Enumerative Combinatorics (vol. 1 & 2) by Richard Stanely

But, its not for the faint of heart.

Maybe van lint's and wilson's book will suit you better, well it depends on the material covered in the course.

## 1. What is combinatorics and graph theory?

Combinatorics is a branch of mathematics that deals with counting, arranging, and selecting objects or elements without repetition. Graph theory is a subfield of combinatorics that studies graphs, which are mathematical structures used to model pairwise relationships between objects.

## 2. Why is combinatorics and graph theory important?

Combinatorics and graph theory have numerous applications in various fields, including computer science, operations research, and statistics. They provide tools and techniques for solving problems involving discrete structures, making them essential in problem-solving and decision-making processes.

## 3. How are combinatorics and graph theory used in real-world problems?

Combinatorics and graph theory are used to solve problems in a wide range of fields, such as network design, scheduling, coding theory, and cryptography. They are also applied in social networks, transportation systems, and biological networks to analyze and understand complex relationships and structures.

## 4. What are some recommended graduate-level texts for studying combinatorics and graph theory?

Some widely used texts for graduate-level combinatorics and graph theory include "Combinatorics and Graph Theory" by John Harris, Jeffry L. Hirst, and Michael S. Mossinghoff, "Introduction to Graph Theory" by Douglas West, and "Enumerative Combinatorics" by Richard P. Stanley.

## 5. What are the prerequisites for studying combinatorics and graph theory at the graduate level?

Typically, a strong background in undergraduate mathematics, including calculus, linear algebra, abstract algebra, and discrete mathematics, is required for studying combinatorics and graph theory at the graduate level. Familiarity with basic concepts in computer science and probability theory is also beneficial.

• Science and Math Textbooks
Replies
6
Views
1K
• Science and Math Textbooks
Replies
8
Views
2K
• Science and Math Textbooks
Replies
1
Views
1K
• Science and Math Textbooks
Replies
10
Views
2K
• Science and Math Textbooks
Replies
2
Views
1K
• Science and Math Textbooks
Replies
1
Views
1K
• Science and Math Textbooks
Replies
5
Views
2K
• Science and Math Textbooks
Replies
1
Views
2K
• Science and Math Textbooks
Replies
33
Views
5K
• Science and Math Textbooks
Replies
4
Views
1K