Undergrad Project Topic: Graph Theory, Combinatorics & Complexity

[Dragonfall]

I'm in my last year as an undergrad (hopefully) and I'm looking for a subject to do an "honours project" on. I actually have no ideas, but maybe someone can suggest a topic in graph theory, combinatorics or complexity?

 

[lordkelvin]

You should talk to some professors you've had who work in your area(s) of interest and ask for some guidance. They might be happy to help you out.

 

[mmmboh]

Well I sure hope he's finished by now!

 

[lordkelvin]

Woah me too! I didn't even realize I bumped something so old lol

 

[rezeew]

I am excited to hear that you are considering a project in the field of graph theory, combinatorics, and complexity for your undergraduate honours project. These are fascinating and rapidly growing areas of research with many potential topics to explore.

One potential topic that comes to mind is the study of random graphs and their properties. Random graphs are mathematical models that help us understand the structure and behavior of real-world networks, such as social networks, computer networks, and biological networks. Your project could involve investigating different models of random graphs and analyzing their properties, such as connectivity, clustering, and degree distribution. This could also involve studying the phase transitions and critical phenomena that occur in random graphs.

Another interesting topic could be the application of graph theory and combinatorics in computer science and data analysis. With the increasing amount of data being generated and collected, efficient algorithms and methods for analyzing and visualizing this data are becoming more and more important. Your project could involve developing new graph-based algorithms for data analysis, or studying the complexity of existing algorithms and their performance on different types of data.

Additionally, you could explore the connections between graph theory and other fields such as physics, biology, and economics. For example, the study of complex networks in biology has led to new insights into the structure and function of biological systems, and the application of graph theory in economics has helped us understand the behavior of markets and social networks.

Ultimately, the best topic for your project will depend on your interests and strengths. I would recommend discussing your ideas with your advisor and other faculty members in your department to get their input and guidance. Good luck with your project, and I am confident that whatever topic you choose, it will be a valuable and rewarding experience.