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Abstract

Random graphs is a generic name for discrete probability spaces, whose ground sets are composed of graphs, or more generally of discrete structures. Since its inception by Erdős and Rényi some sixty years ago, random graphs have grown to be one of the key disciplines in modern Combinatorics, at the same time serving as an indispensable tool for other branches of Combinatorics and Computer Science.

The course will serve as an introduction to random graphs, covering classical topics as well as addressing recent developments and tools.

Course syllabus (tentative): 

Models of random graphs and of random graph processes; illustrative examples; random regular graphs, configuration model; small subgraphs; long paths and Hamiltonicity; hitting time results; coloring problems; extremal problems in random graphs; pseudo-​random graphs.

Desirable background:  

Working knowledge of Graph Theory, familiarity with basic notions of Probability and Linear Algebra.