My main research area is graph theory, in particular some problems in graph coloring, task scheduling or graph searching. A large part of my research is related to the graph ranking problem - this study is motivated by several nice theoretical properties (for example the equivalence with the problem of finding an elimination tree of minimum height, and a strong connection to the problem of searching in partial orders) as well as its potential practical applications in parallel query processing, cholesky factorization of  matrices in parallel or parallel assembly of modular products. In this area I am concentrating on finding efficient algorithms and studying its properties as well as pointing out computationally hard instances. For an overview of the problem and its applications see e.g. my PhD Thesis.

In the field of the graph searching problem I am interested in the topics related to treewidth, pathwidth or elimination trees, as well as the models closely related to the graph ranking problem. In particular, some special cases of searching in partial orders can be reduced to edge ranking of a tree or to finding a minimum edge ranking spanning tree of the graph corresponding to the partial order. The problem of searching in partial orders is interesting both from theoretical and practical point of view - it is a generalization of a binary search in a sorted table and one of the potential applications is related to software testing.

Another area of my scientific interest is combinatorial game theory, especially the computational complexity of games. I have been recently working on the problem of the complexity of the game of phutball and on a rather theoretical game called node blocking - a game related to the family of annihilation games.