General Information

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Project Description

With Aneta Šťastná we work on a topic from graph theory. Under guidance of Sophie Spirkl we study short cycles in graphs. We want to find interesting results about rainbow cycles in general graphs. Our work is motivated by results in directed graphs.

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Weekly Log

Week 1 (6/3-9):

I participated on REU students presentetions. The topics of research are very diverse and interesting. I had my first meeting with our mentor Sophie Spirkl and I started deepen our knowledge about cycles in graphs.

Week 2 (Jun 10-16):

I read few papers about rainbow subgraphs in directed and undirected graphs. We found inspiration in article about short cycles in sparse graphs (Aharoni's conjecture for r = 2).

Week 3 (Jun 17-23):

We had our third meeting with Sophie Spirkl. We discussed our observations about graphs which doesn't contain any short rainbow cycles. And from all ideas we chose few for our next work.

Week 4 (Jun 24-30):

Jie Gao had interesting presentation about applications of artificial intelligence. Dimacs organized a workshop on optimization in distance geometry. I attended tutorials and talks about distance graph coloring, optimization of dynamic systems, reconstruction of structures of molecules, Steiner trees, Euclidean distance problem with interval data and other.

Week 5 (Jul 1-7):

Lazaros had a talk about scientific writing. This week we haven't a meeting with our mentor but we did a valuable progress in study of structure of cuts in graphs without short rainbow cycles.

Week 6 (Jul 8-14):

Previous week helped us to prove with Sophie and Anet a theorem about existence of a short rainbow cycle in special class of graphs. We summarized our research work and presented a part of our results in a talk included in Thursday REU final presentations.

Week 7 (Jul 15-21):

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Presentations

• Rainbow Cycles - Introduction
• Rainbow Cycle - Final presentation