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Research

Research Project

• Asymptotic properties of graphs on a surface
Since the foundation of the theory of random graphs by Erdos and Renyi five decades ago, various random graphs have been introduced and studied. One example is random graphs on a surface, in particular random planar graphs. Graphs on a 2-dimensional surface and related objects (e.g. planar graphs, triangulations) have been among the most studied objects in graph theory, enumerative combinatorics, discrete probability theory, and statistical physics. The main objectives of this project are to study the asymptotic properties and limit behaviour of random graphs on a surface (e.g. evolution, phase transition, critical behaviour, component size distribution) and to investigate enumerative and algorithmic aspects of unlabelled graphs on a surface (e.g. connectivity, symmetry, decomposition, random generation).