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.

Résumé

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.

Contenu

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.