Discrete mathematics, including (combinatorial) number theory and set theory has always been a stronghold of Hungarian mathematics. The present volume honouring Vera Sos and Andras Hajnal contains survey articles (with classical theorems and state-of-the-art results) and cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers inspire further research.

The volume is recommended to experienced specialists as well as to young researchers and students.

Autorentext
László Lovász ist einer der Leiter der theoretischen Forschungsabteilung der Microsoft Corporation. Er hat 1999 den Wolf-Preis sowie den Gödel-Preis für die beste wissenschaftliche Veröffentlichung in der Informatik erhalten.

Inhalt
A Unifying Generalization of Sperner's Theorem.- A Quick Proof of Sprindzhuk's Decomposition Theorem.- Discrepancy in Graphs and Hypergraphs.- Biplanar Crossing Numbers I: A Survey of Results and Problems.- An Exercise on the Average Number of Real Zeros of Random Real Polynomials.- Edge-Connection of Graphs, Digraphs, and Hypergraphs.- Perfect Powers in Products with Consecutive Terms from Arithmetic Progressions.- The Topological Version of Fodor's Theorem.- Color-Critical Graphs and Hypergraphs with Few Edges: A Survey.- Pseudo-random Graphs.- Bounds and Extrema for Classes of Graphs and Finite Structures.- Relaxing Planarity for Topological Graphs.- Notes on CNS Polynomials and Integral Interpolation.- The Evolution of an Idea Gallai's Algorithm.- On the Number of Additive Representations of Integers.- A Lifting Theorem on Forcing LCS Spaces.- Extremal Functions for Graph Minors.- Periodicity and Almost-Periodicity.