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This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes survey articles reviewing classical theorems, as well as new, state-of-the-art results. Also presented are 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 are sure to inspire further research.

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Contents.- Preface.- M. Beck, X. Wang, T. Zaslavsky: A Unifying Generalization of Sperner´s Theorem.- Y.F. Bilu, D. Masser: A Quick Proof of Sprindzhuk´s Decomposition Theorem.- B. Bollobas, A.D. Scott: Discrepancy in Graphs and Hypergraphs.- E. Czabarka, O. Sykora, L.A. Szekely, I. Vrt´o: Biplanar Crossing Numbers I: A Survey of Results and Problems.- C. Doche, M. Mendes France: An Exercise on the Average Number of Real Zeros of Random Real Polynomials.- A. Frank: Edge-Connection of Graphs, Digraphs, and Hypergraphs.- K. Györy: Perfect Powers in Products with Consecutive Terms from Arithmetic Progressions.- I. Juhasz, A. Szymanski: The Topological Version of Fodor´s Theorem.- A. Kostochka: Color-Critical Graphs and Hypergraphs with Few Edges: A Survey.- M. Krivelevich, B. Sudakov: Pseudo-random Graphs.- J. Nesetril: Bounds and Extrema for Classes of Graphs and Finite Structures.- J. Pach, R. Radoicic, G. Toth: Relaxing Planarity for Topological Graphs.- A. Pethö: Notes on CNS Polynominals and Integral Interpolation.- A. Recski, D. Szeszler: The Evolution of an Idea - Gallai´s Algorithm.- A. Sarközy: On the Number of Additive Representations of Integers.- L. Soukup: A Lifting Theorem on Forcing LCS Spaces.- A. Thomason: Extremal Functions for Graph Minors.- A Tijdeman: Periodicity and Almost-Periodicity.

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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.

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