Jakub Cerny

I'm student of Computer science on the Faculty of Maths and Physics of Charles University in Prague. I'm in the fifth year of the study, so I'm finishing my thesis now. I'm interested in graphs, combinatorics, linear algebra and discrete geometry.

I'm working together with Ales, Ida, Jan, Robert, Tomas and Vitek. Our advisor is prof. Joseph Beck. The chief of our Prague group is Robert Samal.

geometric and topological graph

On DIMACS REU I was working on geometric graphs. I started working on them in Prague and here generalize my result. If you are interested in geometric graphs, you can look at slides from my final presentation. The main result is

Theorem: Geometric graph G with n vertices without containing three pairwise disjoint edges has at most 2.5n+7 edges.

This result improves former result by Goddart et al. He proved the upper bound 3n. New bound is tight up to constant, because Perles showed, that there are geometric graphs without three pairwise edges with 2.5n-2 edges. It a nice excercise. Try it.

If you want to see something about other REU project of our czech group, please look at Jan's page.

You can look at my personel homepage, which is ufortunately in czech.
If you are interested in seeing some photos from REU, look at nikam (nowhere in English).