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Ramsey Theory

Unsolved Problems and Results

Xiaodong Xu, Meilian Liang, Haipeng Luo (Autoren)

Buch | Hardcover

XII, 178 Seiten

2018
De Gruyter (Verlag)
978-3-11-057651-1 (ISBN)

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Key problems and conjectures have played an important role in promoting the development of Ramsey theory, a field where great progress has been made during the past two decades, with some old problems solved and many new problems proposed. The present book will be helpful to readers who wish to learn about interesting problems in Ramsey theory, to see how they are interconnected, and then to study them in depth. This book is the first problem book of such scope in Ramsey theory. Many unsolved problems, conjectures and related partial results in Ramsey theory are presented, in areas such as extremal graph theory, additive number theory, discrete geometry, functional analysis, algorithm design, and in other areas. Most presented problems are easy to understand, but they may be difficult to solve. They can be appreciated on many levels and by a wide readership, ranging from undergraduate students majoring in mathematics to research mathematicians. This collection is an essential reference for mathematicians working in combinatorics and number theory, as well as for computer scientists studying algorithms. ContentsSome definitions and notationsRamsey theoryBi-color diagonal classical Ramsey numbersPaley graphs and lower bounds for R(k, k)Bi-color off-diagonal classical Ramsey numbersMulticolor classical Ramsey numbersGeneralized Ramsey numbersFolkman numbersThe Erdős–Hajnal conjecture Other Ramsey-type problems in graph theory On van der Waerden numbers and Szemeredi’s theorem More problems of Ramsey type in additive number theory Sidon–Ramsey numbers Games in Ramsey theory Local Ramsey theory Set-coloring Ramsey theory Other problems and conjectures

Xiaodong Xu and Haipeng Luo, Guangxi Academy of Science, China; Meilian Liang, Guangxi University, China

Erscheinungsdatum	05.08.2018
Co-Autor	University of Science & Technology
Zusatzinfo	10 b/w ill., 20 b/w tbl.
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	170 x 240 mm
Gewicht	450 g
Themenwelt	Mathematik / Informatik ► Mathematik
Themenwelt	Recht / Steuern ► Steuern / Steuerrecht
Schlagworte	Algebra • CINE8 • combinatorial analysis • combinatorics • Combinatorics and graph theory • graph theory • Mathematics • Mathematik • METAPHORISIEREN • Number Theory • Ramsey theory • Schmitt
ISBN-10	3-11-057651-1 / 3110576511
ISBN-13	978-3-11-057651-1 / 9783110576511
Zustand	Neuware