Institute of Optimization and Discrete Mathematics

Research Grants

Phase Transitions in Random Graphs and Random Graph Processes

The objectives of this project are to study the phase transitions in random graphs and random graph processes with constraints such as degree distribution, forbidden substructures, genus. The phase transition is a phenomenon observed in many fundamental problems from statistical physics, mathematics and theoretical computer science, including Potts models, graph colourings and satisfiability problem. The phase transition observed in the plethora of different random graph models refers to a phenomenon that there is a critical value of edge density such that adding a small number of edges around the critical value results in a dramatic change in the size of the largest components. It is our aim to further develop and apply new analytic approaches combined with counting and probabilistic methods, e.g. singularity analysis, differential equations method, to the study of the phase transitions in random graphs and random graph processes.

• supported by German Research Foundation (DFG), Grant no. KA 2748/3-1, 01.10.2011-30.09.2014
• Institute's members in this project: Mihyun Kang (Principal Investigator), Angélica Pachón (Postdoctoral Researcher)

Doctoral Program Discrete Mathematics

The institute of Optimization and Discrete Mathematics takes part in the Doctoral Program "Discrete Mathematics", which offers an advanced PhD training and research program.

• supported by Austrian Science Fund (FWF), Grant no. W 1230-N13, 2010-
• Institute's members in this project: Ante Ćustić (Doctoral Student), Clemens Heuberger (Principal Investigator), Mihyun Kang (Associated Scientist), Bettina Klinz (Principal Investigator), Daniel Krenn (Doctoral Student)