# Place to find exercises in Graph Theory

Currently I'm studying Graph Theory and have noticed, that it really helps my understanding to try to do many exercises. I have currently run out of exercises and am now looking for recommendations for books/websites/other places to find exercises on Graph Theory. I have worked my way through Reinhard Diesel's book on Graph theory and I am specifically looking for exercises covering topics like:

• connectivity
• matchings
• Eulerian/Hamiltonian cycles
• Planar graphs
• graph colorings

If anyone has a suggestion for sources with exercises related to these topics, I would be happy to hear it :-)

• The Cambridge Tripos Part II questions for the last two decades are available and typically include several Graph Theory questions. For example, there were four such questions this summer. Commented Aug 1 at 14:06
• I checked out West ( 8 Chapters ) to see around $200 + 140 + 100 + 100 + 100 + 80 +90 +250 \approx 1050$ Exercises. It covers your list.
– Prem
Commented Aug 1 at 14:53
• Thank you! You mean Introduction to Graph Theory by Douglas West, I suppose?
– Immi
Commented Aug 1 at 15:18
• That was what I meant. You should use the "AT Character" like this , @Immi , to alert the concerned user , otherwise the user may not know that you commented.
– Prem
Commented Aug 1 at 15:59
• Okay, thank you! @Prem
– Immi
Commented Aug 1 at 16:01

Your judgement that graph theory is best learnt from exercises seems very accurate - it is a visual topic, best learnt by drawing graphs out, colouring nodes in, and figuring out how definitions look. When I did a graph theory course at university, there were a few tools which helped. Some are textbooks with problems, lecture notes with exercises, or quite importantly are graph theory tasks to have a go at using programming (since this is one of the core applications of graph theory). The following resources are not extensive, but should give you somewhere to start.

1. Introduction to Graph Theory by Richard J. Trudeau: A short textbook which covers most areas of fundamental graph theory, with plenty of exercises at the end of each chapter. See here: https://www.amazon.co.uk/Introduction-Graph-Theory-Dover-Mathematics/dp/0486678709
2. Exercises in Graph Theory by O. Melnikov: A textbook which acts as a supplement to the respective authors lecture notes graph theory book. It is rammed full of a variety of exercises. See here: https://www.amazon.co.uk/Exercises-Graph-Theory-Mathematical-Sciences/dp/0792349067
3. Supplementary Exercises to Introduction to Graph Theory by Douglas B. West: Douglas B. West wrote a textbook on graph theory, and his personal website has enormous numbers of graph theory exercises. It is likely impossible to work your way through all of these! They’re freely available. See here: https://dwest.web.illinois.edu/igt/newprob.html
4. MIT OpenCourseware Lecture Series on Graph Theory and Additive Combinatorics: A lecture course on graph theory delivered by Prof. Yufei Zhao. There are 11 pages of assignment problems to work through, again freely available. See here: https://ocw.mit.edu/courses/18-217-graph-theory-and-additive-combinatorics-fall-2019/
5. Oxford lecture series on Graph Theory: Oxford University’s open source mathematic resources boast five problem sheets to work through. Some may be quite challenging since they’re aimed at Oxford students so represent a good extension activity to attempt. See here: https://courses.maths.ox.ac.uk/course/view.php?id=659
6. Cambridge Tripos Problem Sheets: Years worth of problem sheets used for the graph theory course at Cambridge University. See here: https://www.dpmms.cam.ac.uk/study/II/Graphs/previous.html
7. Leetcode Graph Problems: A vast list of exercises to work through relating to graph theory and programming. See here: https://leetcode.com/tag/graph/

These resources span the great depths of graph theory - covering all of the topics you mentioned. If you want to only cover connectivity, matchings, Hamiltonian cycles, planar graphs, and graph colourings - you are always able to skip to the relevant problem sheets or chapters.

Best of luck! If you have any further questions about the resources, feel free to ask.

New contributor
TopologyTitan is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.