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AG Audience

English

30 Minutes

Saarbrücken

The phase transition deals with sudden global changes and is observed in many fundamental problems from statistical physics, mathematics and theoretical computer science, for example, Potts models, graph colourings and random k-SAT. The phase transition in random graphs refers to a phenomenon that there is a critical edge density, to which adding a small amount a drastic change in the size of the largest component occurs. In Erd{\H o}s-R\'enyi random graph, which begins with an empty graph on $n$ vertices and edges are added randomly one at a time to a graph, a phase transition takes place when the number of edges reaches $n/2$ and a giant component emerges. Since this seminal work of Erd{\H o}s and R\'enyi, various random graph models have been introduced and studied. In this talk we discuss phase transitions in several random graph models, including Erd{\H o}s-R\'enyi random graph, random graphs with a given degree sequence, random graph processes and random planar graphs.

Konstantinos Panagiotou

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