The subject of the research is discrete optimization problems encountered during graph modeling of systems. The research focuses on the design and analysis of new models and algorithms solving selected problems in various operating modes. We study offline, online and distributed algorithms. In particular, we concentrate on the following issues:

- computational complexity of algorithms and quality of approximation,
- partitions and independence in graphs and hypergraphs,
- extremal structures and selected local properties,
- classical coloring with restrictions for colors on paths,
- agent algorithms for searching and evacuation in graphs.

In the area of potential applications of our research, among others, we cover

- resource constrained task scheduling,
- selected problems of network routing,
- simulating parallel computing architectures,
- modeling frequency/resource allocation in mobile networks,
- problems of automation and optimization of parallel assembly,
- modeling the evacuation and gathering of autonomous robots.

The above research is conducted both for classical graphs with static structure and for graphs whose structure changes over time (temporal graphs).