Hello! I am the graduate coordinator of the Czech group participating in the Research Experience for Undergraduates at DIMACS, Rutgers. We are from DIMATIA, Charles University in Prague. The other members are Ondra Bílka, Tomáš Gavenčiak, Zuzka Safernová, Petr Škoda, Jan Volec, and a graduate student Vítek Jelínek.

We are working under the supervision of Mario Szegedy, Dan Cranston and Padmini Mukkamala.

I study Computer science -- Discrete Models and Algorithms on the Faculty of Maths and Physics of Charles University. I am in the second year of the PhD study. My interests are graph theory, combinatorics, computational complexity and stable matchings. My thesis copes with the computational complexity of Seidel's switching of graphs.

We are working together on the following problems.

This problem is described in detail on Tomáš's website. The problem is contained in the paper Chromatic Number, Independence Ratio, and Crossing Number by M. O. Albertson. Very recently, the problem was solved independently by D. Král' and L. Stacho.

This problem is described in detail on Jan's website. Currently, we are writing up several our results and observations we made.

This problem is described in detail on
Zuzka's website.
It is related to the problem of estimating the number of *k*-sets of a configuration
of points in the plane. There are several papers (collected by
Vítek) that are related to it.

- Convex Quadrilaterals and k-Sets (2003) (Lovasz et al.)
- On k-sets, convex quadrilaterals, and the rectilinear crossing number of K_n (2004) (Balogh, Salazar)
- New Lower Bounds for the Number of (≤k)-Edges and the Rectilinear Crossing Number of Kn (Aichholzer et al.)
- New results on lower bounds for the number of ≤k-facets (Aichholzer et al.)
- Geometric Drawings of K_n with Few Crossings (Abrego, Fernandez-Merchant)

This problem is described in detail on Ondra's website.

This problem is described in detail on Tomáš's website. These are several papers related to it:

- Digraph Measures: Kelly Decompositions, Games, and Orderings by P. Hunter and S. Kreutzer
- Characterization and recognition of digraphs of bounded Kelly-width by D. Meister et al.

You may also want to visit my homepage.

My presentation about the Czech language during REU 2004.

Some more or less useful phrases in Czech.