Summer School on Algebraic and Enumerative Combinatorics

Lectures by Marc Noy

S. Miguel de Seide, Portugal

Topic: Asymptotic enumeration of topological graphs

• Planar maps and Tutte’s decomposition. Enumeration of 2- and 3-connected maps. Whitney’s theorem.
• Enumeration of labelled graphs. Decomposition into blocks and 3-connected components.
• Analytic methods in enumeration.
• Enumeration of outerplanar and series-parallel graphs.
• Enumeration of planar graphs.
• Combinatorial parameters and probability limit laws.
• Random graphs through counting. Basic parameters.
• Extremal parameters.
• Graphs on surfaces and graph minors.